Related papers: On a universal mapping class group of genus zero

A finitely generated group $G$ is said to be condensed if its isomorphism class in the space of finitely generated marked groups has no isolated points. We prove that every product variety $\mathcal{UV}$, where $\mathcal{U}$ (respectively,…

The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.

We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.

For any positive integer $n$, we exhibit a cofinite subgroup $\Gamma_n$ of the mapping class group of a surface of genus at most two such that $\Gamma_n$ admits an epimorphism onto a free group of rank $n$. We conclude that…

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…

We study the bounded cohomology of certain groups acting on the Cantor set. More specifically, we consider the full group of homeomorphisms of the Cantor set as well as Thompson's group $V$. We prove that both of these groups are boundedly…

In this paper we introduce an exponential map of the algebra of germs of vector fields into the group of germs of diffeomorphisms at zero. It is shown that this mapping is not a bijection. A brief review of the key results of the analytic…

Let $S$ be a nonorientable surface of genus $g\ge 5$ with $n\ge 0$ punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\Mcg(S)$. Suppose that $S_1$ and…

Birman-Lubotzky-McCarthy proved that any abelian subgroup of the mapping class groups for orientable surfaces is finitely generated. We apply Birman-Lubotzky-McCarthy's arguments to the mapping class groups for non-orientable surfaces. We…

We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces can not be measure equivalent. Moreover,…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

We provide new constraints for algebro-geometric subgroups of mapping class groups, namely images of fundamental groups of curves under complex algebraic maps to the moduli space of smooth curves. Specifically, we prove that the restriction…

We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

Finite-sheeted covering mappings onto compact connected groups are studied. It is shown that a finite-sheeted covering mapping from a connected Hausdorff topological space onto a compact connected abelian group G must be a homeomorphism…

By analyzing known presentations of the pure mapping groups of orientable surfaces of genus $g$ with $b$ boundary components and $n$ punctures, we show that these groups are isomorphic to some groups related to the braid groups and the…

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We…

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. In the published version of "Mapping class group and a global Torelli theorem for hyperkahler manifolds" I made an error based on a…