Related papers: Small index subgroups of the mapping class group

We prove that if a normal subgroup of the extended mapping class group of a closed surface has an element of sufficiently small support then its automorphism group and abstract commensurator group are both isomorphic to the extended mapping…

The goal of these notes is to prove that the mapping class groups of a closed orientable surface of genus two, with punctures, are not K\"ahler

For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.

In this work we compute the first integral cohomology of the pure mapping class group of a non-orientable surface of infinite topological type and genus at least 3. To this purpose, we also prove several other results already known for…

We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators.

We determine the largest (i.e. smallest index) characteristic subgroup of surface groups not containing any simple loops.

We show that a 3-manifold containing an incompressible surface has topologically minimal surfaces of arbitrary high genus.

We prove that the mapping class group of a closed connected orientable surface of genus at least eight is generated by three involutions.

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by three involutions for $g\geq 6$.

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

Let $N_{g,n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $M(N_{g,n})$ its mapping class group. We obtain an explicit finite presentation of $M(N_{g,n})$ for $n=0,1$ and all $g$ such that $g+n>3$.

We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to $\mathbb{Z}$ factors through a sphere with finitely…

We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces can not be measure equivalent. Moreover,…

We prove that the minimal nontrivial finite quotient group of the mapping class group M_g of a closed orientable surface of genus g is the symplectic group PSp(2g,Z_2), for g = 3 and 4 (this might remain true, however, for arbitrary genus g…

Let $X$ be a Riemann surface, and let $f:X\to\mathbb{P}^1_\mathbb{C}$ be an indecomposable (branched) covering of genus $g$ and degree $n$ whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we…

We classify homomorphisms from mapping class groups by using finite subgroups. First, we give a new proof of a result of Aramayona--Souto that homomorphisms between mapping class groups of closed surfaces are trivial for a range of genera.…

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…

We report on the computation of the integral homology of the mapping class group of genus g surfaces with one boundary curve and m punctures, when 2g + m is smaller than 6. In particular, it includes the genus 2 case with no or one…

There exist right angled Artin groups $A$ such that the isomorphism problem for finitely presented subgroups of $A$ is unsolvable, and for certain finitely presented subgroups the conjugacy and membership problems are unsolvable. It follows…

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…