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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Equivariant topological complexity

Hellen Colman and Mark Grant

Algebraic & Geometric Topology 12 (2012) 2299–2316
Abstract

We define and study an equivariant version of Farber’s topological complexity for spaces with a given compact group action. This is a special case of the equivariant sectional category of an equivariant map, also defined in this paper. The relationship of these invariants with the equivariant Lusternik–Schnirelmann category is given. Several examples and computations serve to highlight the similarities and differences with the nonequivariant case. We also indicate how the equivariant topological complexity can be used to give estimates of the nonequivariant topological complexity.

Keywords
equivariant LS–category, equivariant sectional category, equivariant topological complexity
Mathematical Subject Classification 2010
Primary: 55M99, 57S10
Secondary: 55M30, 55R91
References
Publication
Received: 2 May 2012
Revised: 2 August 2012
Accepted: 4 August 2012
Published: 8 January 2013
Authors
Hellen Colman
Department of Mathematics
Wright College
4300 N. Narragansett Avenue
Chicago, IL 60634
United States
http://faculty.ccc.edu/hcolman/
Mark Grant
School of Mathematical Sciences
The University of Nottingham
University Park
Nottingham, NG7 2RD
United Kingdom
http://www.maths.nottingham.ac.uk/personal/pmzmg/