Big mapping class groups: an overview
arXiv:2003.07950 · doi:10.1007/978-3-030-55928-1_12
Abstract
We survey recent developments on mapping class groups of surfaces of infinite topological type.
v3: Proposition 4.12---as numbered in v2---was false and has been deleted in this version. v2: added cover image (illustration by Juan Pablo Díaz González), fixed typos, corrected/added references, rectified imprecisions. v1: To appear as a chapter in the forthcoming volume "In the tradition of Thurston". Comments welcome!
References in corpus (25)
- Geometry of the Complex of Curves I: Hyperbolicity
- Bounded cohomology of subgroups of mapping class groups
- The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
- Train tracks and the Gromov boundary of the complex of curves
- Uniform hyperbolicity of the curve graph via surgery sequences
- Large scale geometry of big mapping class groups
- The first integral cohomology of pure mapping class groups
- Commensurations of the Johnson kernel
- Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire
- Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group
- Algebraic and topological properties of big mapping class groups
- Continuity of discrete homomorphisms of diffeomorphism groups
- Homomorphisms between mapping class groups
- Graphs of curves on infinite-type surfaces with mapping class group actions
- Isometry groups of infinite-genus hyperbolic surfaces
- Automatic continuity for homeomorphism groups and applications
- An infinite genus mapping class group and stable cohomology
- Wild translation surfaces and infinite genus
- Nielsen realization for infinite-type surfaces
- Diffeomorphisms groups of tame Cantor sets and Thompson-like groups
- Structure theorems for actions of homeomorphism groups
- Loxodromic elements in big mapping class groups via the Hooper-Thurston-Veech construction
- Big mapping class groups acting on homology
- Geometric normal subgroups in mapping class groups of punctured surfaces
- First cohomology of pure mapping class groups of big genus one and zero surfaces
Cited by in corpus (23)
- The first integral cohomology of pure mapping class groups
- Isometry groups of infinite-genus hyperbolic surfaces
- Nielsen realization for infinite-type surfaces
- Most big mapping class groups fail the Tits Alternative
- Mapping class groups with the Rokhlin property
- Braided Thompson groups with and without quasimorphisms
- First integral cohomology group of the pure mapping class group of a non-orientable surface of infinite type
- Large-Scale Geometry of Pure Mapping Class Groups of Infinite-Type Surfaces
- Homological stability for the ribbon Higman--Thompson groups
- Generating the liftable mapping class groups of regular cyclic covers
- Curve graphs of surfaces with finite-invariance index 1
- Big mapping class groups with uncountable integral homology
- Three perfect mapping class groups
- Asymptotic mapping class groups of Cantor manifolds and their finiteness properties
- On the homology of big mapping class groups
- Infinite-type loxodromic isometries of the relative arc graph
- Towards Nielsen-Thurston classification for surfaces of infinite type: well-tempered homeomorphisms
- A class of open surfaces with algorithmically solvable homeomorphism problem
- Twisted Rokhlin property for mapping class groups
- Compact and finite-type support in the homology of big mapping class groups
- Non-planar ends are continuously unforgettable
- An Alexander method for infinite-type surfaces
- Infinite-dimensional Teichm{ü}ller spaces