Compact and finite-type support in the homology of big mapping class groups

Abstract

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 to study this question, in particular giving an almost-complete answer when the genus of $S$ is positive (including infinite) and a partial answer when the genus of $S$ is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces.

arXiv comment24 pages, 5 figures. Final version, to appear in the Journal of the London Mathematical Society

References in corpus (7)

• Stabilization for mapping class groups of 3-manifolds
• Low-dimensional homology groups of mapping class groups: a survey
• Big mapping class groups: an overview
• Bounded cohomology and binate groups
• Lagrangian mapping class groups from a group homological point of view
• Big mapping class groups with uncountable integral homology
• On the homology of big mapping class groups