相关论文: On endomorphisms of surface mapping class groups

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group…

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from a sphere to an orthogonal or a unitary group is homotopic…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.

We survey recent developments on mapping class groups of surfaces of infinite topological type.

We prove that if a normal subgroup of the extended mapping class group of a closed surface has an element of sufficiently small support then its automorphism group and abstract commensurator group are both isomorphic to the extended mapping…

Let $N$ be a connected nonorientable surface of genus $g$ with $n$ punctures. Suppose that $g$ is odd and $g+n \geqslant 6$. We prove that the automorphism group of the complex of curves of $N$ is isomorphic to the mapping class group…

We show that the group of class-preserving automorphisms of a universal hyperlinear group has index 2 inside the group of all automorphisms.

For each of the 14 classes of edge-transitive maps described by Graver and Watkins, necessary and sufficient conditions are given for a group to be the automorphism group of a map, or of an orientable map without boundary, in that class.…

This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle group inclusions, and of Lucchini on generators for special…

In this article we study automorphisms and endomorphisms of lacunary hyperbolic groups. We prove that every lacunary hyperbolic group is Hopfian, answering a question by Henry Wilton. In addition, we show that if a lacunary hyperbolic group…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics.…

We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…