Homotopy types of Diffeomorphism groups of noncompact 2-manifolds
Geometric Topology
2009-11-12 v3 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0109183,
title = {Homotopy types of Diffeomorphism groups of noncompact 2-manifolds},
author = {Tatsuhiko Yagasaki},
journal= {arXiv preprint arXiv:math/0109183},
year = {2009}
}
Comments
27 pages, Definition 3.1 is corrected