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 (4)
Cited by in corpus (21)
- Isometry groups of infinite-genus hyperbolic surfaces
- Nielsen realization for infinite-type surfaces
- Mapping class groups with the Rokhlin property
- Most big mapping class groups fail the Tits Alternative
- Braided Thompson groups with and without quasimorphisms
- Large-Scale Geometry of Pure Mapping Class Groups of Infinite-Type Surfaces
- First integral cohomology group of the pure mapping class group of a non-orientable surface of infinite type
- 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
- Infinite-type loxodromic isometries of the relative arc graph
- Asymptotic mapping class groups of Cantor manifolds and their finiteness properties
- On the homology of big mapping class groups
- Infinite-dimensional Teichm{ü}ller spaces
- Towards Nielsen-Thurston classification for surfaces of infinite type: well-tempered homeomorphisms
- An Alexander method for infinite-type surfaces
- Compact and finite-type support in the homology of big mapping class groups
- Non-planar ends are continuously unforgettable
- Twisted Rokhlin property for mapping class groups