Related papers: Subgroups of the mapping class group from the geom…
We construct a map from fundamental groups of complements to some plane configurations to the groups $G_{n}^{k}$ for large $k$. We discuss connection between the groups $G_{n}^{k}$ for different $G_{n}^{k}$ and their geometric realization.
We prove the Congruence Subgroup Property for two families of subgroups of Mapping Class Groups of finite-type surfaces. The first one is related to nilpotent quotients of the fundamental group and Johnson filtration, and along the way we…
We give the first part of a proof of Thurston's Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a ``Lipschitz model'' for the thick part of the corresponding hyperbolic…
We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes.
Suppose subgroups $A,B < MCG(S)$ in the mapping class group of a closed orientable surface $S$ are given and let $\langle A, B \rangle$ be the subgroup they generate. We discuss a question by Minsky asking when $\langle A, B \rangle \simeq…
Let T(N) be the subgroup of the mapping class group of a nonorientable surface N (possibly with punctures and/or boundary components) generated by twists about two-sided circles. We obtain a simple generating set for T(N). As an application…
A random graph of free groups contains a surface subgroup
Let $X$ be a minimal cubic surface over a finite field $\mathbb{F}_q$. The image $\Gamma$ of the Galois group $\operatorname{Gal}(\overline{\mathbb{F}}_q / \mathbb{F}_q)$ in the group $\operatorname{Aut}(\operatorname{Pic}(\overline{X}))$…
We describe the subgroup of the mapping class group of a hypersurface in $\mathbb{CP}^4$ consisting of those diffeomorphisms which can be realised by monodromy.
We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This…
We obtain a minimal generating set of involutions for the level 2 subgroup of the mapping class group of a closed nonorientable surface.
We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology representation.
We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.
We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty…
The mapping class group of a non-exceptional oriented surface of finite type admits a biautomatic structure.
This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is…
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
This paper unifies the concept of kinematic mappings by using geometric algebras. We present a method for constructing kinematic mappings for certain Cayley-Klein geometries. These geometries are described in an algebraic setting by the…
We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.
Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup…