Related papers: The mapping class group is generated by two commut…
The mapping class group of a Heegaard splitting is the group of automorphisms of the ambient 3-manifold that take the surface onto itself, modulo isotopies that keep the surface on itself. We characterize the mapping classes that restrict…
For a closed surface $S$, its Torelli group $\mathcal{I}(S)$ is the subgroup of the mapping class group of $S$ consisting of elements acting trivially on $H_1(S;\mathbb{Z})$. When $S$ is orientable, a generating set for $\mathcal{I}(S)$ is…
In this paper we define a $\mathbf{QP}^1$-valued class function on the mapping class group $\mathcal{M}_{g,2}$ of a surface $\Sigma_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a $\Sigma_{g,2}$ bundle over a pair of pants…
Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it fixes a point.
A modular fusion category C allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then C has a unique Morita-class of simple…
The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of $\Sigma$, and let $\MM (\Sigma,…
It is well known that Sullivan showed that the mapping class group of a simply connected high-dimensional manifold is commensurable with an arithmetic group, but the meaning of "commensurable" in this statement seems to be less well known.…
Let $M$ be a closed surface. By $\Homeo(M)$ we denote the group of orientation preserving homeomorphisms of $M$ and let $\MC(M)$ denote the Mapping class group. In this paper we complete the proof of the conjecture of Thurston that says…
We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to…
The mapping class group of a non-exceptional oriented surface of finite type admits a biautomatic structure.
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 exhibit a finitely generated group $\M$ whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface $\su$ of infinite genus, and…
We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…
We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…
Omori and the author have given an infinite presentation for the mapping class group of a compact non-orientable surface. In this paper, we give more simple infinite presentations for this group.
We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orbits has infinite diameter. This applies, for instance, to…
In this paper we deal with the class C of decomposable solvable Lie groups having dimension at most six. We determine those Lie groups in C and their subgroups which are the multiplication group Mult(L) and the inner mapping group Inn(L)…
Consider a surface $S$ and let $M\subset S$. If $S\setminus M$ is not connected, then we say $M$ \emph{separates} $S$, and we refer to $M$ as a \emph{separating set} of $S$. If $M$ separates $S$, and no proper subset of $M$ separates $S$,…
Let $S$ be a closed orientable hyperbolic surface, and let $\mathcal{O}(K,S)$ denote the number of mapping class group orbits of curves on $S$ with at most $K$ self-intersections. Building on work of Sapir [16], we give upper and lower…
Let $S_{g}$ denote the genus $g$ closed orientable surface. For $k\in \mathbb{N}$, a $k$-system is a collection of pairwise non-homotopic simple closed curves such that no two intersect more than $k$ times. Juvan-Malni\v{c}-Mohar…