Work

On the homology of big mapping class groups

Year: 2024

Type: article

Abstract: We prove that the mapping class group of the one‐holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once‐punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite‐type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite‐type surfaces.

Source: Journal of Topology

DOI: 10.1112/topo.12358

Authors: Martin Palmer, Xiaolei Wu

Institutions: IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române, Fudan University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Fudan University, Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii