Automatic continuity for homeomorphism groups of noncompact manifolds

2020/03/02 by Kathryn Mann, Mann, Kathryn
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.2003.01173

arxiv created 2020/03/02 · arxiv updated 2020/03/04

Abstract

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold M homeomorphic to the interior of a compact manifold, and a set X ⊂ M homeomorphic to the union of a Cantor set and finite set, the relative homeomorphism group Homeo(M, X) and the mapping class group Homeo(M, X)/Homeo₀(M,X) have the property that any homomorphism from such a group to any separable topological group is necessarily continuous.

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