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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]

Let the pair ( G , M ) R denote a group G acting on an R -module M , R a unitary ring. We ask for the existence of an R -local space X such that ( E ( X ) , π k ( X ) ) R is equivalent, in a natural way, to ( G , M ) R , for some k ≥ 2 , where E ( X ) denotes the group of homotopy classes of self-homotopy equivalences of X . If such an X exists, we say that X realizes the group action ( G , M ) R . We prove that if G is finite and acts faithfully on a finitely generated Q -module M , there exist infinitely many rational spaces realizing ( G , M ) Q . Our proof relies on providing a positive answer to Kahn's realizability problem for a large class of orthogonal groups that strictly contains finite ones. As a matter of fact, we enlarge the class of groups that is known to be realizable in the classical Kahn's sense. [ABSTRACT FROM AUTHOR]

We show that the vertex coloring problem for finite simplicial complexes can be translated into the algebraic homotopy problem of ellipticity for rational spaces. We follow the ideas of Lechuga-Murillo for the classical vertex coloring of graphs. [ABSTRACT FROM AUTHOR]

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]

We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear in a separate paper. [ABSTRACT FROM AUTHOR]