Homotopy types of homeomorphism groups of noncompact 2-manifolds

Details Homotopy types of homeomorphism groups of noncompact 2-manifolds Homotopy types of homeomorphism groups of noncompact 2-manifolds

2000-10-24

arxiv.org/abs/math/0010223v1

Mathematics

Geometric Topology

13 pages

Scientific paper

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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