## Algebraic & Geometric Topology

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

Marja Kankaanrinta

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 1 (2007), 1-27.

Dates
Revised: 30 October 2006
Accepted: 4 December 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796653

Digital Object Identifier
doi:10.2140/agt.2007.7.1

Mathematical Reviews number (MathSciNet)
MR2289802

Zentralblatt MATH identifier
1181.57037

Subjects
Primary: 57S20: Noncompact Lie groups of transformations

#### Citation

Kankaanrinta, Marja. Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions. Algebr. Geom. Topol. 7 (2007), no. 1, 1--27. doi:10.2140/agt.2007.7.1. https://projecteuclid.org/euclid.agt/1513796653

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