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We produce examples of pairwise non-diffeomorphic closed irreducible 4-manifolds with non-trivial free abelian fundamental group of rank less than three and small Euler characteristic. These exotic smooth structures become standard after taking a connected sum with a single copy of $S^2\times S^2$. The contributions of this paper include an explicit mechanism to computate the equivariant intersection form of 4-manifolds that are obtained via torus surgeries and a new stabilization result concerning exotic smooth structures with arbitrary fundamental group.

Motivated by the duality theory between Hermitian symmetric spaces of noncompact and compact types, we introduce and examine the concept of K\"ahler duality between domains of $\mathbb C^n$., Comment: 33 pages

What is certain is that surface temperatures around the globe vary considerably, regardless of the time scales or underlying causes. Since 1850, we have observed an average increase in global surface temperature anomalies of 1.2$^{\circ}$ and a median increase of 0.7$^{\circ}$: this overall difference masks significant regional differences. Nearly 60\% of the world's population now lives in urban areas, where vegetation cover has been significantly reduced, despite the paradoxical fact that vegetation plays an important role in regulating the thermal environment (\textit{eg} through the shading provided by tree canopies). Continuous electrical and thermal measurements of trees in a Parisian grove (France) show and quantify that canopies are not the only protectors against heat waves; we must also consider the role of tree trunks. It is clear that these trunks probably regulate themselves, possibly by modulating the uptake of groundwater, whose geothermal stability is well established at a depth of just one meter. This quantitative observation should not be overlooked in the urban planning of our cities., Comment: 15 pages, 6 figures

In this paper, we revisit old electrical measurements conducted on a poplar tree in 2003 (Gibert et al. 2006), which showed the presence of a diurnal electrical signal, attributed to an electrokinetic phenomenon correlated with sap flow, even in winter. We reanalyze these data using the singular spectrum analysis method and demonstrate that the electrical signal measured at various locations (roots, trunk, and branches) on the poplar tree can be decomposed to over 80\% into a sum of 7 pseudo-periods, all linked to luni-solar tides. The precision of the extracted periods exceeds that of models. To validate these old measurements, we have reproduced the 2003 protocol since 2018 at the Jardin des Plantes in Paris, on 3 oak trees and 3 hornbeams. The electrical signals today exhibit the same characteristics as those of 2003. Tidal forces could be a driving force of sap flow in trees., Comment: 22 pages, 7 figures

In this lengthy letter, we wanted to discuss the concept of climate based on definitions established for over a century and direct observations that we have been collecting for more than a century as well. To do this, we present and discuss the remarkably stable maps over time of the various physical parameters that make up the climate corpus: solar temperature, atmospheric pressure, winds, precipitation, temperature anomalies. This impressionistic tableau that we are gradually sketching as our reflection unfolds leads us to the following proposition: What if, as Laplace first proposed in 1799 and later Milankovi\{'}c in 1920, ground temperature were merely a consequence of climate and not a separate parameter of climate in its own right?, Comment: 24 pages, 11 Figures

The periodical degassing from CO2 over-pressured reservoirs may have serious consequences for the environment making urgent understanding the processes and forecasting the frequency. Prediction though needs methods that depends from temporal and spatial properties of hydro-chemical and physical reservoir characteristics that unfortunately are often lacking. We have analyzed surface emissions of CO2 attributed to over-pressured CO2-rich reservoirs in the Central Italian Apennines a zone characterized by significant periodical CO2 degassing. Here aquifers are hosted in Mesozoic limestone with high pCO2 groundwater and travertine deposits. We analyzed a 10-year temporal series and found that in the Apennines, CO2 flux and aquifer fluid composition are correlated with the lunar tides specific to the geographic zone. In particular, our study reveals that low CO2 flux corresponds with low lunar tidal potential values. We found a similar trend for dissolved calcium and water alkalinity, while pH values display a linear correlation with tidal cycles. The forces associated with tidal potentials are not capable of fracturing rock. However, they can, under certain conditions, drive the flow of fluids in over-pressured reservoirs, triggering sub-surface fluid movements that in turn modify the water-rock reactivity. In the central Apennines, these movements result in increased dolomite dissolution and an eventual return to calcite equilibrium. In this case, dolomite dissolution breaks the rock releasing calcium into ground water, which leads to calcite equilibrium and in turn to the formation of significant quantities of travertine and the concomitant release of CO2 in the atmosphere., Comment: 12 pages, 6 figures

The trajectory of Earth about the Sun is perturbed by torques exerted by the Moon and Sun, and also the four giant planets. These provoke variations of insolation at Earth surface, known as kyr-long Milankovi\'c cycles. The concept has been extended to the shorter time scales of years to centuries, that are relevant to tree growth. This paper focuses on iSSA of results of the dendro-chronological study of a forest of long-lived Tibetan junipers. From this, we determine a median curve of tree growth rates, that is analyzed by iSSA. We obtain a rich set of (pseudo-) periods, from 3.3 yr up to more than 1000 years, that compare with the specific spectral signature found in the sunspot and length-of-day time series. We discuss in detail the record from a single tree that spans almost completely the 357-2000 AD interval. The 90 yr Gleissberg, 22 yr and 30 yr components are quite prominent. The Oort, Wolf, Sp\"orer, Maunder and Dalton climate extrema all correspond quite precisely to extrema of the Gleissberg cycle. The well-known Medieval Climate Optimum, Little Ice Age and Modern Climate Optimum all seem to be mainly forced by variations in the envelope of the Gleissberg cycle. The Gleissberg cycle is strongly modulated with a period of 500-600 years. The node near a small gap in the data is very close to the Medieval Climate Optimum. Observations in different parts of Earth are in favor of a global extension of the MCO. In the same way that the Milankovic mathematical theory of climate allows one to relate climate change and length of day, through changes in inclination of Earth's rotation axis and solar insolation, it is reasonable to propose that the set of pseudo-periods that are evidenced in the Tibetan tree ring growth rates simply corresponds to short period Milankovi\'c cycles. The Dulan forest could be considered as a good candidate for a continuous, global geophysical observatory., Comment: 26 pages, 15 figures

The decryption of the temporal sequence of volcanic eruptions is a key step in better anticipating future events. Volcanic activity is the result of a complex interaction between internal and external processes, with time scales spanning multiple orders of magnitude. We review periodicities that have been detected or correlated with volcanic eruptions/phenomena and interpreted as resulting from external forces. Taking a global perspective and longer time scales than a few years, we approach this interaction by analyzing three time series using singular spectral analysis: the global number of volcanic eruptions (NVE) between 1700 and 2022, the number of sunspots (ISSN), a proxy for solar activity, the polar motion (PM) and length of day (lod), two proxies for gravitational force. Several pseudo-periodicities are common to NVE and ISSN, in addition to the 11-year Schwabe cycle that has been reported in previous work, but NVE shares even more periodicities with PM. These quasi-periodic components range from ~5 to ~130 years. We interpret our analytical results in light of the Laplace's paradigm and propose that, similarly to the movement of Earth's rotation axis, global eruptive activity is modulated by commensurable orbital moments of the Jovian planets, whose influence is also detected in solar activity.

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting., Comment: 6 pages

Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold with associated Delzant polytope $\Delta$ and Ehrhart polynomial $P_\Delta$ such that $P_{\Delta}=P_{\lambda\Sigma_n}$, for some $\lambda \in \mathbb{Z}^+$, then $(M, L)\cong (\mathbb{C} P^n, O(\lambda))$ (where $O(1)$ is the hyperplane bundle on $\mathbb{C} P^n$) in the following three cases: 1. arbitrary $n$ and $\lambda=1$, 2. $n=2$ and $\lambda =3$, 3. $\lambda =n+1$ under the assumption that the polarization $L$ is asymptotically Chow semistable., Comment: 10 pages

We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that for a Reeb function we can prescribe the set of minima (or maxima), as soon as this set is a PL subcomplex of the manifold. In analogy with Reeb's Sphere Theorem, we use such functions to study the topology of the underlying manifold. In dimension $3$, we give a characterization of manifolds having a Heegaard splitting of genus $g$ in terms of the existence of certain Reeb functions. Similar results are proved in dimension $n\geq 5$.

We prove that a radial Kaehler metric g is Kaehler-Einstein if and only if one of the following conditions is satisfied: 1. g is extremal and it is associated to a Kaehler-Ricci soliton; 2. two different generalized scalar curvatures of g are constant; 3. g is extremal (not cscK) and one of its generalized scalar curvature is constant., Comment: 11 pages. arXiv admin note: text overlap with arXiv:2105.10695

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and not complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the triviality of a KRS induced by a finite dimensional complex space form proved in [12] does not hold when the ambient space is allowed to be infinite dimensional. Moreover, we show that the radial potential of a radial KRS induced by a non-elliptic complex space form is necessarily defined at the origin., Comment: 22 pages

Automatic generators of GUI tests often fail to generate semantically relevant test cases, and thus miss important test scenarios. To address this issue, test adaptation techniques can be used to automatically generate semantically meaningful GUI tests from test cases of applications with similar functionalities. In this paper, we present ADAPTDROID, a technique that approaches the test adaptation problem as a search-problem, and uses evolutionary testing to adapt GUI tests (including oracles) across similar Android apps. In our evaluation with 32 popular Android apps, ADAPTDROID successfully adapted semantically relevant test cases in 11 out of 20 cross-app adaptation scenarios.

We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural with respect to spin structures. In particular this solves Problem 4.113(C) in Kirby's list. We also discuss analogous results for other families of 4-manifolds with infinite fundamental groups., Comment: 11 pages. Updated to reflect solution to Kirby Problem 4.113(C)

We establish the method of holomorphic handle attaching to the strongly pseudoconcave boundary of a complex surface. We use this for proving the following statements: (1) every closed connected oriented contact 3-manifold can be filled as the strongly pseudoconcave boundary of a compact complex surface; (2) any two closed connected oriented contact 3-manifolds are complex cobordant. Moreover, we show that such complex surface (or complex cobordism) can be taken K\"ahler., Comment: 13 pages

In this paper we address the problem of studying those complex manifolds $M$ equipped with extremal metrics $g$ induced by finite or infinite dimensional complex space forms. We prove that when $g$ is assumed to be radial and the ambient space is finite dimensional then $(M, g)$ is itself a complex space form. We extend this result to the infinite dimensional setting by imposing the strongest assumption that the metric $g$ has constant scalar curvature and is well-behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kaehler-Einstein metrics induced by infinite dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant non-positive holomorphic sectional curvature., Comment: 24 pages

Inspired by the work of Z. Lu and G. Tian \cite{lutian}, in this paper we address the problem of studying those \K\ manifolds satisfying the $\Delta$-property, i.e. such that on a neighborhood of each of its points the $k$-th power of the \K Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer $k$ (see below for its definition). We prove two results: 1. if a \K\ manifold satisfies the $\Delta$-property then its curvature tensor is parallel; 2. if an Hermitian symmetric space of classical type satisfies the $\Delta$-property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a complete and simply-connected \K\ manifold satisfies the $\Delta$-property then it is a complex space form., Comment: 13 pages

We show that the Ricci flat Calabi's metrics on holomorphic line bundles over compact Kaehler-Einstein manifolds are not projectively induced. As a byproduct we solve a conjecture addressed in [arXiv:1705.03908v2 [math.DG]] by proving that any multiple of the Eguchi-Hanson metric on the blow-up of C^2 at the origin is not projectively induced., Comment: 10 pages

F. Podest\`a and A. Spiro introduced a class of $G$-manifolds $M$ with a cohomogeneity one action of a compact semisimple Lie group $G$ which admit an invariant Kaehler structure $(g,J)$ (``standard $G$-manifolds") and studied invariant Kaehler and Kaehler-Einstein metrics on $M$. In the first part of this paper, we gave a combinatoric description of the standard non compact $G$-manifolds as the total space $M_{\varphi}$ of the homogeneous vector bundle $M = G\times_H V \to S_0 =G/H$ over a flag manifold $S_0$ and we gave necessary and sufficient conditions for the existence of an invariant Kaehler-Einstein metric $g$ on such manifolds $M$ in terms of the existence of an interval in the $T$-Weyl chamber of the flag manifold $F = G \times _H PV$ which satisfies some linear condition. In this paper, we consider standard cohomogeneity one manifolds of a classical simply connected Lie group $G = SU_n, Sp_n. Spin_n$ and reformulate these necessary and sufficient conditions in terms of easily checked arithmetic properties of the Koszul numbers associated with the flag manifold $S_0 = G/H$. If this conditions is fulfilled, the explicit construction of the Kaehler-Einstein metric reduces to the calculation of the inverse function to a given function of one variable., Comment: 27 pages

Let $(M, g)$ be a Kaehler manifold whose associated Kaehler form $\omega$ is integral and let $(L, h)\rightarrow (M, \omega)$ be a quantization hermitian line bundle. In this paper we study those Kaehler manifolds $(M, g)$ admitting a finite TYCZ expansion. We show that if the TYCZ expansion is finite then $T_{mg}$ is indeed a polynomial in $m$ of degree $n$, $n=dim M$, and the log-term of the Szeg\"{o} kernel of the disc bundle $D\subset L^*$ vanishes (where $L^*$ is the dual bundle of $L$). Moreover, we provide a complete classification of the Kaehler manifolds admitting finite TYCZ expansion either when $M$ is a complex curve or when $M$ is a complex surface with a cscK metric which admits a radial Kaehler potential.

In this paper we adopt an alternative, analytical approach to Arnol'd problem \cite{A1} about the existence of closed and embedded $K$-magnetic geodesics in the round $2$-sphere $\mathbb S^2$, where $K: \mathbb S^2 \rightarrow \mathbb R$ is a smooth scalar function. In particular, we use Lyapunov-Schmidt finite-dimensional reduction coupled with a local variational formulation in order to get some existence and multiplicity results bypassing the use of symplectic geometric tools such as the celebrated Viterbo's theorem and Bottkoll results., Comment: 27 pages. To appear in Manuscripta Mathematica

We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data., Comment: 6 pages

Given a constant $k>1$ and a real valued function $K$ on the hyperbolic plane $\mathbb H^2$, we study the problem of finding, for any $\epsilon\approx 0$, a closed and embedded curve $u^\epsilon $ in $\mathbb H^2$ having geodesic curvature $k+\epsilon K(u^\epsilon)$ at each point., Comment: Theorems numbering has been changed; few misprints were fixed

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures., Comment: 16 pages, 11 figures

We classify radial scalar flat metrics with constant third coeffcient of its TYZ expansion. As a byproduct of our analysis we provide a characterization of Simanca's scalar flat metric., Comment: 14 pages

In this paper we prove that the closed $4$-ball admits non-K\"ahler complex structures with strictly pseudoconcave boundary. Moreover, the induced contact structure on the boundary $3$-sphere is overtwisted., Comment: 11 pages, 0 figure

We give necessary and sufficient conditions for a 4-manifold to be a branched covering of $CP^2$, $S^2\times S^2$, $S^2 \mathbin{\tilde\times} S^2$ and $S^3 \times S^1$, which are expressed in terms of the Betti numbers and the intersection form of the 4-manifold., Comment: 18 pages, 1 figure, 29 references

Inspired by the analogous result in the algebraic setting (Theorem 1) we show (Theorem 2) that the product $M \times \mathbb{R}P^n$ of a closed and orientable topological manifold $M$ with the $n$-dimensional real projective space cannot be topologically locally flat embedded into $\mathbb{R}P^{m + n + 1}$ for all even $n > m$., Comment: To appear in Topology and its Applications

We propose two conjectures about Ricci-flat metrics: Conjecture 1: A Ricci-flat projectively induced metric is flat. Conjecture 2: A Ricci-flat metric on an $n$-dimensional complex manifold such that the $a_{n+1}$ coefficient of the TYZ expansion vanishes is flat. We verify Conjecture 1 (see Theorem 1.1) under the assumptions that the metric is radial and stable-projectively induced and Conjecture 2 (see Theorem 1.2) for complex surfaces whose metric is either radial or complete and ALE. We end the paper by showing, by means of the Simanca metric, that the assumption of Ricci-flatness in Conjecture 1 and in Theorem 1.2 cannot be weakened to scalar-flatness (see Theorem 1.3)., Comment: To appear in Mathematische Zeitschrift

We find necessary and sufficient conditions under which the complex coordinates on a flag manifold of a classical group described in [2] are Bochner coordinates., Comment: 24 pages

Let $M$ be a cohomogeneity one manifold of a compact semisimple Lie group $G$ with one singular orbit $S_0 = G/H$. Then $M$ is $G$- diffeomorphic to the total space $G \times_H V$ of the homogeneous vector bundle over $S_0$ defined by a sphere transitive representation of $G$ in a vector space $V$. We describe all such manifolds $M$ which admit an invariant Kahler structure of standard type. This means that the restriction $\mu: S = Gx = G/L \rightarrow F = G/K$ of the moment map of $M$ to a regular orbit $S = G/L$ is a holomorphic map of $S$ with the induced CR structure onto a flag manifold $F = G/K$, where $K = N_G(L)$, endowed with an invariant complex structure $J^F$ . We describe all such standard Kahler cohomogeneity one manifolds in terms of the painted Dynkin diagram associated with $(F=G/K; J^F)$ and a parametrized interval in some T-Weyl chamber. We determine which of these manifolds admit invariant Kahler-Einstein metrics.

We provide new branched covering representations for bounded and/or non-compact 4-manifolds, which extend the known ones for closed 4-manifolds. Assuming $M$ to be a connected oriented PL 4-manifold, our main results are the following: (1) if $M$ is compact with (possibly empty) boundary, there exists a simple branched cover $p:M \to S^4 - \mathop{\mathrm{Int}}(B^4_1 \cup \dots \cup B^4_n)$, where the $B^4_i$'s are disjoint PL 4-balls, $n \geq 0$ is the number of boundary components of $M$; (2) if $M$ is open, there exists a simple branched cover $p : M \to S^4 - \mathop{\mathrm{End}} M$, where $\mathop{\mathrm{End}} M$ is the end space of $M$ tamely embedded in $S^4$. In both cases, the degree $d(p)$ and the branching set $B_p$ of $p$ can be assumed to satisfy one of these conditions: (1) $d(p)=4$ and $B_p$ is a properly self-transversally immersed locally flat PL surface; (2) $d(p)=5$ and $B_p$ is a properly embedded locally flat PL surface. In the compact (resp. open) case, by relaxing the assumption on the degree we can have $B^4$ (resp. $R^4$) as the base of the covering. We also define the notion of branched covering between topological manifolds, which extends the usual one in the PL category. In this setting, as an interesting consequence of the above results, we prove that any closed oriented topological 4-manifold is a 4-fold branched covering of $S^4$. According to almost-smoothability of 4-manifolds, this branched cover could be wild at a single point., Comment: 16 pages, 9 figures

We follow our study of non-K\"ahler complex structures on $R^4$ that we defined in a previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without K\"ahler metrics., Comment: Minor revision

We compute the Gromov width of homogeneous Kaehler manifolds with second Betti number equal to one. Our result is based on the recent preprint [4] and on the upper bound of the Gromov width for such manifolds obtained in [6]., Comment: 3 pages

We construct the first examples of non-K\"ahler complex structures on $R^4$. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann., Comment: 9 pages, 3 figures, minor revision, Definition 1 has been changed

Let $M$ be a projective toric manifold. We prove two results concerning respectively Kaehler-Einstein submanifolds of M and symplectic embeddings of the standard euclidean ball in M. Both results use the well-known fact that M contains an open dense subset biholomorphic to C^n., Comment: 20 pages