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

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

2000-10-24

arxiv.org/abs/math/0010224v1

Mathematics

Geometric Topology

18 pages

Scientific paper

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 (s^infty,sigma^infty,sigma^infty_f)-manifold and determine its topological type. We also study the subgroups of Lipschitz homeomorphisms.

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