Related papers: Classifying spaces for proper actions of mapping c…
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.
Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper…
We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group $\mbox{Mod}(S)$ of any connected oriented compact surface $S$, possibly…
We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…
We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…
We show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed…
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
The mapping class group of a compact oriented surface of genus greater than one with boundary acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group, for every choice of…
In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of…
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…
The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
We prove that the mapping class group of a closed surface acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group.
We derive two types of linearity conditions for mapping class groups of orientable surfaces: one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case, the condition is described in terms of…
Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action…
This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface $S$. We describe a quadratic time algorithm for the word problem in this group, which can be…
We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.
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…
We give a bound for the geometric dimension for the family of virtually cyclic groups in mapping class groups of a compact surface with punctures, possibly with nonempty boundary and negative Euler characteristic.
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…