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Abstract Let M be a closed n -dimensional manifold, n > 2 , whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form α on M , closed but non-exact, and a pseudo-gradient X such that the differential ∂ X of the Novikov complex of the pair (α , X) has at least one incidence coefficient which is an infinite series. This is an application of our previous study of the homoclinic bifurcation of pseudo-gradients of multivalued Morse functions. [ABSTRACT FROM AUTHOR]

We establish a formality theorem for smooth dg manifolds. More precisely, we prove that, for any finite-dimensional dg manifold ( M , Q ) , there exists an L ∞ quasi-isomorphism of dglas from ( T poly • ⊕ ( M ) , [ Q , − ] , [ − , − ] ) to ( D poly • ⊕ ( M ) , 〚 m + Q , − 〛 , 〚 − , − 〛 ) whose first Taylor coefficient (1) is equal to the composition hkr ∘ ( td ( M , Q ) ∇ ) 1 2 : T poly • ⊕ ( M ) → D poly • ⊕ ( M ) of the action of ( td ( M , Q ) ∇ ) 1 2 ∈ ∏ k ≥ 0 ( Ω k ( M ) ) k on T poly • ⊕ ( M ) (by contraction) with the Hochschild–Kostant–Rosenberg map and (2) preserves the associative algebra structures on the level of cohomology. As an application, we prove the Kontsevich–Shoikhet conjecture: a Kontsevich–Duflo-type theorem holds for all finite-dimensional smooth dg manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we classify b m -Nambu structures via b m -cohomology. The complex of b m -forms is an extension of the De Rham complex, which allows us to consider singular forms. b m -Cohomology is well understood thanks to Scott (2016) [12] , and it can be expressed in terms of the De Rham cohomology of the manifold and of the critical hypersurface using a Mazzeo–Melrose-type formula. Each of the terms in b m -Mazzeo–Melrose formula acquires a geometrical interpretation in this classification. We also give equivariant versions of this classification scheme. [ABSTRACT FROM AUTHOR]

With any g -manifold M are associated two dglas tot ( Λ • g ∨ ⊗ k T poly • ( M ) ) and tot ( Λ • g ∨ ⊗ k D poly • ( M ) ) , whose cohomologies H CE • ( g , T poly • ( M ) → 0 T poly • + 1 ( M ) ) and H CE • ( g , D poly • ( M ) → d H D poly • + 1 ( M ) ) are Gerstenhaber algebras. We establish a formality theorem for g -manifolds: there exists an L ∞ quasi-isomorphism Φ : tot ( Λ • g ∨ ⊗ k T poly • ( M ) ) → tot ( Λ • g ∨ ⊗ k D poly • ( M ) ) whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the g -manifold M , and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the g -manifold M is an isomorphism of Gerstenhaber algebras from H CE • ( g , T poly • ( M ) → 0 T poly • + 1 ( M ) ) to H CE • ( g , D poly • ( M ) → d H D poly • + 1 ( M ) ) . [ABSTRACT FROM AUTHOR]

Let ( M , F ) be a compact boundaryless Finsler manifold. In this work, a sufficient condition for a vector field on ( M , F ) to be harmonic is obtained. Next the harmonic vector fields on Finsler manifolds are characterized and an upper bound for the first horizontal de Rham cohomology group of the sphere bundle SM is obtained. [ABSTRACT FROM AUTHOR]

Let ( M , F ) be a compact boundaryless Landsberg manifold. In this work, a necessary and sufficient condition for a vector field on ( M , F ) to be harmonic is obtained. Next, on a compact boundaryless Finsler manifold of zero flag curvature, a necessary and sufficient condition for a vector field to be harmonic is found. Furthermore, the nonexistence of harmonic vector fields on a compact Landsberg manifold is studied and an upper bound for the first de Rham cohomology group is obtained. [ABSTRACT FROM AUTHOR]

Abstract: I study the dynamical degrees of automorphisms of a compact Kähler manifold X of dimension 3 and, more generally, the type of growth of the norm of , where denotes the action of the automorphism f on the cohomology of X. The automorphisms of complex tori show that the results are optimal. [Copyright &y& Elsevier]

Abstract: We prove that a closed differential form of bidimension on a projective manifold is cohomologous to an algebraic cycle with complex coefficients if and only if it is a weak limit of such cycles. This allows us to approach the problem of the algebraicity of cohomology classes. Using the characterization of currents associated with algebraic cycles by the Chow transform, the obstructions are reduced to an orthogonality condition with certain smooth functions on the Grassmannian, which are in general merely images of distributions by a suitable explicitly defined linear differential operator. These distributions are of order less than k. This forces a convergence in the space of functions, which is achieved, when the cohomology class is rational, thanks to the constructibility of the Bernstein polynomial. [Copyright &y& Elsevier]

Abstract: In studying the Bott–Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott–Chern q-complete manifolds. [Copyright &y& Elsevier]

Abstract: The subdivision of the cell decomposition of a Seifert manifold yields a Δ-simplicial decomposition and a quasi-isomorphism. We exhibit Δ-simplicial cocycles that lift the usual cellular generators of the cohomology of the manifold. Applying the Alexander–Whitney formula, this allows one to describe explicitly the cohomology ring structure of this Seifert manifold with coefficients in , p prime. [Copyright &y& Elsevier]