Related papers: Simple infinite presentations for the mapping clas…

We show that several families of asymptotically rigid mapping class groups arise as explicit quotients of the fundamental group of a graph of groups, with mapping class groups as vertex and edge stabilizers. Using this description, and…

We give presentations of braid groups and pure braid groups on surfaces.

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary) of the closed unit disk with a sequence of interior…

Even though big mapping class groups are not countably generated, certain big mapping class groups can be generated by a coarsely bounded set and have a well defined quasi-isometry type. We show that the big mapping class group of a stable…

We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…

We analyze the number of ends of the mapping class group of a stable avenue surface. We prove that the mapping class group is one-ended whenever the stable avenue surface has at least one end of discrete type. Our method is to show that the…

We simplify construction of Thoma representations of an infinite symmetric group

We study the mapping class group of a nontrivial irreducible shift of finite type: the group of flow equivalences of its mapping torus modulo isotopy. This group plays for flow equivalence the role that the automorphism group plays for…

We answer two questions about the topology of end spaces of infinite type surfaces and the action of the mapping class group that have appeared in the literature. First, we give examples of infinite type surfaces with end spaces that are…

For a genus g handlebody H a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H, is constructed and several properties are established. In particular, this complex naturally contains, as a…

Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus…

We develop a theory of generalized presentations of groups. We give generalized presentations of the symmetric group $\Sigma(X)$ for an arbitrary set $X$ and of the automorphism group of the free group of countable rank, $Aut(F_{\omega})$.

We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…

Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup…

This paper has 3 principal goals: (1) to survey what is know about mapping class and Torelli groups of simply connected compact Kaehler manifolds, (2) supplement these results, and (3) present a list of questions and open problems to…

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.

We give the canonical normal form for the elements of the finite or infinite alternating groups using local stationary presentation of these groups.

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to…