Volume 7, issue 1 (2007)

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Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions

Marja Kankaanrinta

Algebraic & Geometric Topology 7 (2007) 1–27
Abstract

The purpose of this paper is to prove equivariant versions of some basic theorems in differential topology for proper Lie group actions. In particular, we study how to extend equivariant isotopies and then apply these results to obtain equivariant smoothing and gluing theorems. We also study equivariant collars and tubular neighbourhoods. When possible, we follow the ideas in the well-known book of M W Hirsch. When necessary, we use results from the differential topology of Hilbert spaces.

Keywords
smooth, proper action, Lie group, collar, gluing
Mathematical Subject Classification 2000
Primary: 57S20
References
Publication
Received: 19 January 2006
Revised: 30 October 2006
Accepted: 4 December 2006
Published: 23 February 2007
Authors
Marja Kankaanrinta
Department of Mathematics
PO Box 400137
University of Virginia
Charlottesville VA 22904-4137
USA