Related papers: A note on subgroups of the Loch Ness Monster Surfa…
We describe computer calculations that were used in 2016 to classify subgroups of the Monster isomorphic to $PSL_2(8)$, containing $7B$-elements. It turns out that there is no such $PSL_2(8)$ in the Monster. These calculations confirm…
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.
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…
For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…
For every countable group $G$, there are $2^{\omega}$ distinct classes of coarsely equivalent subsets of $G$.
We describe the subgroup of the mapping class group of a hypersurface in $\mathbb{CP}^4$ consisting of those diffeomorphisms which can be realised by monodromy.
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly…
A topological group $(G,\mu)$ from a class $\mathcal G$ of MAP topological abelian groups will be called a {\it Mackey group} in $\mathcal G$ if it has the following property: if $\nu$ is a group topology in $G$ such that $(G,\nu)\in…
Every locally compact local group is locally isomorphic to a topological group.
In this article, we prove that every finite abelian group $G$ of odd order occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
We prove that, for any infinite-type surface $S$, the integral homology of the closure of the compactly-supported mapping class group $\overline{\mathrm{PMap}_c(S)}$ and of the Torelli group $\mathcal{T}(S)$ is uncountable in every positive…
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 show the details of certain computations that are described in [BMW19].
The theme of this survey is that subgroups of the mapping class group of a finite type surface S can be studied via the geometric/dynamical properties of their action on the Thurston compactification of the Teichmuller space of S, just as…
We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.
Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…
We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.