Related papers: Big mapping class groups acting on homology
We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
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…
Let S be a compact orientable surface with genus g and n boundary components d_1,...,d_n. Let b = (b_1, ..., b_n) where b_n lies in [-2,2]. Then the mapping class group of S acts on the relative SU(2)-character variety X comprising…
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…
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…
In this paper, we introduce two new classes of representations of the framed braid groups. One is the homological representation constructed as the action of a mapping class group on a certain homology group. The other is the monodromy…
We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.
We show that the mapping class group of a handlebody of genus at least 2 (with any number of marked points or spots) is exponentially distorted in the mapping class group of its boundary surface. The same holds true for solid tori with at…
In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct interesting actions…
It has been known since the time of Nielsen that the mapping class group $\text{Mod}_{g,1}$ of a surface of genus $g$ and one puncture acts faithfully by homeomorphisms on the circle. In this note, we show that this standard representation…
We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step…
This is a long introduction to the theory of "branch groups": groups acting on rooted trees which exhibit some self-similarity features in their lattice of subgroups.
We let the mapping class group $\Gamma_{g,1}$ of a genus $g$ surface $\Sigma_{g,1}$ with one boundary component act on the homology $H_*(F_{n}(\Sigma_{g,1});\mathbb{Q})$ of the $n^{th}$ ordered configuration space of the surface. We prove…
In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…
In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…
In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
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…
The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…
Let $\Gamma_{g,1}^m$ be the mapping class group of the orientable surface $\Sigma_{g,1}^m$ of genus $g$ with one parametrised boundary curve and $m$ permutable punctures; when $m=0$ we omit it from the notation. Let…