Homotopy types of Diffeomorphism groups of noncompact 2-manifolds

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

2001-09-24

arxiv.org/abs/math/0109183v3

Mathematics

Geometric Topology

27 pages, Definition 3.1 is corrected

Scientific paper

Suppose M is a noncompact connected smooth 2-manifold without boundary and let D(M)_0 denote the identity component of the diffeomorphism group of M with the compact-open C^infty-topology. In this paper we investigate the topological type of D(M)_0 and show that D(M)_0 is a topological ell_2-manifold and it has the homotopy type of the circle if M is the plane, the open annulus or the open M"obius band, and it is contractible in all other cases. When M admits a volume form w, we also discuss the topological type of the group of w-preserving diffeomorphisms of M. To obtain these results we study some fundamental properties of transformation groups on noncompact spaces endowed with weak topology.

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