The groups of PL and Lipschitz homeomorphisms of noncompact 2-manifolds

2000/10/24 by Tatsuhiko Yagasaki, Yagasaki, Tatsuhiko
Mathematics · #57N05 #57N20 #58B05 #58D15 #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #math.GN #math.GT #msc:57N05 #msc:57N20 #msc:58B05 #msc:58D15

paper · pdf · doi:10.48550/arxiv.math/0010224

18 pages

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

Abstract

Suppose M is a noncompact connected PL 2-manifold. In this paper we study the topological property of the triple (H(M)₀, H^PL(M)₀, H^PL, c(M)₀), where H(M)₀ is the identity component of the homeomorphism group \cal H(M) of M with the compact-open topology, and H^PL(M)₀ and H^PL, c(M)₀ are the identity components of the subgroups consisting of PL-homeomorphisms of M and ones with compact supports. We show that this triple is a (sⁱnfty,sigmaⁱnfty,sigmaⁱnfty_f)-manifold and determine its topological type. We also study the subgroups of Lipschitz homeomorphisms.

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