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Equivariant topological
complexity
Hellen Colman and Mark Grant |
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Algebraic & Geometric Topology 12 (2012) 2299–2316
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 55M99, 57S10
Secondary: 55M30, 55R91
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References |
Publication
Received: 2 May 2012
Revised: 2 August 2012
Accepted: 4 August 2012
Published: 8 January 2013
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Authors |
| Hellen Colman | |
| Department of Mathematics Wright College 4300 N. Narragansett Avenue Chicago, IL 60634 United States |
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| http://faculty.ccc.edu/hcolman/ | |
| Mark Grant | |
| School of Mathematical
Sciences The University of Nottingham University Park Nottingham, NG7 2RD United Kingdom |
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| http://www.maths.nottingham.ac.uk/personal/pmzmg/ | |
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