相关论文: On Nielsen equivalence classes of two-elements gen…

We prove that the extended mapping class group is generated by three orientation reversing involutions.

It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping…

The mapping class group of a non-exceptional oriented surface of finite type admits a biautomatic structure.

For any positive integer $n$, we exhibit a cofinite subgroup $\Gamma_n$ of the mapping class group of a surface of genus at most two such that $\Gamma_n$ admits an epimorphism onto a free group of rank $n$. We conclude that…

S. Bigelow proved that the braid groups are linear. That is, there is a faithful representation of the braid group into the general linear group of some field. Using this, we deduce from previously known results that the mapping class group…

We demonstrate the existence of numerous non-spin 4-manifolds for which the smooth Nielsen realization problem fails; namely, there exist finite subgroups of their mapping class groups that cannot be realized by any group of…

The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classes of intersection points and essential classes of…

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…

In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a sparse collection of simple closed curves on an orientable surface are right angled Artin…

We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.

We show that for all $n \equiv 0 \pmod{6}$, $n \geq 18$, there is an orientable triangular embedding of the octahedral graph on $n$ vertices that can be augmented with handles to produce a genus embedding of the complete graph of the same…

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.

A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact…

In this note we prove that the mapping class group of a compact topological manifold $M$ with boundary is of finite type, under assumptions on its dimension and connectivity.

Two free homotopy classes of closed curves in an orientable surface with negative Euler characteristic are said to be length equivalent if for any hyperbolic structure on the surface, the length of the geodesic in one class is equal to the…

We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.

In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface normally generates the (pure) mapping class group of the…

Let $\Gamma_g$ denote the orientation-preserving Mapping Class Group of the genus $g\geq 1$ closed orientable surface. In this paper we show that for fixed $g$, every finite group occurs as a quotient of a finite index subgroup of…

Let $S_g$ denote the closed orientable surface of genus $g$. We construct exponentially many mapping class group orbits of collections of $2g+1$ simple closed curves on $S_g$ which pairwise intersect exactly once, extending a result of the…

We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then…