Related papers: Separable subgroups of mapping class groups

The theme of this survey is that subgroups of the mapping class group of a finite type surface S can be studied via the geometric/dynamical properties of their action on the Thurston compactification of the Teichmuller space of S, just as…

This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The…

This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_{\sigma}$ of a compact closed surface $X$ of genus $\sigma$ is considered. A complete method of enumeration is achieved for…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…

Let $D$ be a division ring. In this paper, we investigate properties of subgroups of an arbitrary subnormal subgroup of the multiplicative group $D^*$ of $D$. The new obtained results generalize some previous results on subgroups of $D^*$.

In this short note we give an elementary proof of the fact that every countable group is a subgroup of the mapping class group of the Loch Ness monster 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 prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.

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…

We study mapping cones and their dual cones of positive maps of the n by n matrices into itself. For a natural class of cones there is a close relationship between maps in the cone, super-positive maps, and separable states. In particular…

The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and…

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 classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.

We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).

The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are discussed.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping…