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An oriented closed connected $N$ -manifold $M$ is inflexible if it does not admit self-maps of unbounded degree. In addition, if all the maps from any other oriented closed connected $N$ -manifold have bounded degree, then $M$ is said to be strongly inflexible. The existence of simply-connected inflexible manifolds was established by Arkowitz and Lupton. However, the existence of simply-connected strongly inflexible manifolds is still an open question. We provide an algorithm relying on Sullivan models that allows us to prove that all, but one, of the known examples of simply-connected inflexible manifolds are not strongly inflexible. [ABSTRACT FROM AUTHOR]

In this paper we show that evolution algebras over any given field \Bbbk are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X)\cong G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme \mathbf {G} over \Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra. [ABSTRACT FROM AUTHOR]

Ovarian fibromatosis (OF) is a rare non-neoplastic condition, more frequent in young females and characterised by ovarian enlargement with proliferation of collagen-producing spindle cells in the stroma. It usually presents with abdominal pain, menstrual disorders or as a solid mass. Hirsutism and virilisation are possible. The relevance of this subject remains in the usual misdiagnosis as a malignant tumour, which may lead to unnecessary oophorectomies. We report the case of a 17-year-old female who presented with acute intense pain in the right iliac fossa and vomits. On examination, she complained of intense pain without any signs of peritonism. An abdominal ultrasound was performed, finding an enlarged right adnexal containing a heterogenic cyst without flow to the ovary. A Pfannenstiel laparotomy showed a right ovarian torsion. The haemorrhagic cyst was drained and the ovary was detorsed. Bilateral ovarian biopsies were performed as both ovaries showed an indurated and cerebroid surface, suggestive of malignancy. Tumoural markers were negative. Histological examination confirmed OF. After 3 months, the magnetic resonance imaging showed an enlarged right ovary with a fibrous capsule surrounding both ovaries. In conclusion, OF can also be found incidentally in the context of an ovarian torsion. Since its appearance may be dismissed as malignant, it is important to recognise it and remain conservative. Biopsies can be taken to make the differential diagnosis. [ABSTRACT FROM AUTHOR]

Let X be a finite type An2-polyhedron, n ≥ 2. In this paper, we study the quotient group ℰ (X) / ℰ*(X), where ℰ (X) is the group of self-homotopy equivalences of X and ℰ*(X) the subgroup of self-homotopy equivalences inducing the identity on the homology groups of X. We show that not every group can be realised as ℰ (X) or ℰ (X) / ℰ *(X) for X an An2-polyhedron, n ≥ 3, and specific results are obtained for n = 2. [ABSTRACT FROM AUTHOR]

Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant between the classical LS cocategory and the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to characterize finite homotopy nilpotent loop spaces in the spirit of Hubbuck's Torus Theorem, and obtain corresponding results for p-compact groups and p-Noetherian groups. [ABSTRACT FROM AUTHOR]

Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ1 (X) along rX: X → Bπ1 (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of rX (or the ‘almost’ p-localization of X) is a fibrewise co-H-space (or an ‘almost’ co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of Bπ1 (X) along rX, X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space. [ABSTRACT FROM PUBLISHER]

We prove that the isomorphism type of a large class of groups is determined by the class of differential graded algebras over an integral domain with mild conditions, on which these groups act faithfully. [ABSTRACT FROM PUBLISHER]