Non-planar ends are continuously unforgettable

2024/09/09 by Aramayona, Javier, De Pool, Rodrigo, Skipper, Rachel +3
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2409.05502

Abstract

We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups.

Related

• Epimorphisms of 3-manifold groups
• The mapping class group cannot be realized by homeomorphisms
• Big mapping class groups and the co-Hopfian property
• On cofinite subgroups of mapping class groups
• Isomorphisms between big mapping class groups