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Mapping class groups of surfaces with noncompact boundary components

Ryan Dickmann

Algebraic & Geometric Topology 23 (2023) 2777–2821
Abstract

We show that the pure mapping class group is uniformly perfect for a certain class of infinite-type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete classification of the perfect and uniformly perfect pure mapping class groups for infinite-type surfaces. We also develop a method to cut a general surface into simpler surfaces and extend some mapping class group results to the general case.

Keywords
mapping class group, infinite-type surface, noncompact boundary
Mathematical Subject Classification
Primary: 57K20, 57S05
Secondary: 57M07
References
Publication
Received: 2 April 2021
Revised: 6 March 2022
Accepted: 17 April 2022
Published: 7 September 2023
Authors
Ryan Dickmann
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Department of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States

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