Related papers: Mapping class groups of surfaces with noncompact b…
We completely classify the orientable infinite-type surfaces $S$ such that $\operatorname{PMap}(S)$, the pure mapping class group, has automatic continuity. This classification includes surfaces with noncompact boundary. In the case of…
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…
We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by the second author [15].
We survey recent developments on mapping class groups of surfaces of infinite topological type.
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 show that the closure of the compactly supported mapping class group of an infinite type surface is not perfect and that its abelianization contains a direct summand isomorphic to an uncountable direct sum of rationals. We also extend…
We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.
We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…
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.
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 show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…
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.
We investigate the problem of when big mapping class groups are generated by involutions. Restricting our attention to the class of self-similar surfaces, which are surfaces with self-similar ends space, as defined by Mann and Rafi, and…
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…
Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…
We describe a cocompact model for the classifying space for proper actions of the mapping class group of a surface with punctures and boundary components. Our construction relies on a known model for the case of a closed surface and uses an…
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.
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with…
For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is…
It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger…