Algebraic & Geometric Topology

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

Marja Kankaanrinta

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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

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

Received: 19 January 2006
Revised: 30 October 2006
Accepted: 4 December 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S20: Noncompact Lie groups of transformations

smooth proper action Lie group collar gluing


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.

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