Mapping class groups of surfaces with noncompact boundary components

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.

arXiv comment40 pages, 13 figures. v2: Several minor changes/incorporated referee comments. Accepted to Algebraic and Geometric Topology

References in corpus (6)

• The first integral cohomology of pure mapping class groups
• Algebraic and topological properties of big mapping class groups
• Automatic continuity for homeomorphism groups and applications
• Automatic continuity for homeomorphism groups of noncompact manifolds
• Proper actions on finite products of quasi-trees
• The mapping class group of a disk with infinitely many holes