Homotopy types of homeomorphism groups of noncompact 2-manifolds

2000/10/24 by Tatsuhiko Yagasaki, Yagasaki, Tatsuhiko · 1 citation
Mathematics · #57N05 #57N20 #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #math.GN #math.GT #msc:57N05 #msc:57N20

paper · pdf · doi:10.48550/arxiv.math/0010223

13 pages

arxiv created 2000/10/24 · arxiv updated 2009/11/30

Abstract

Suppose M is a noncompact connected PL 2-manifold and let H(M)₀ denote the identity component of the homeomorphism group of M with the compact-open topology. In this paper we classify the homotopy type of H(M)₀ by showing that \cal H(M)₀ has the homotopy type of the circle if M is the plane, an open or half open annulus, or the punctured projective plane. In all other cases we show that H(M)₀ is homotopically trivial.

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