Equivariant topological complexity

Colman, Hellen¹ ; Grant, Mark²

¹Department of Mathematics, Wright College, 4300 N. Narragansett Avenue, Chicago, IL 60634, United States
²School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2299-2316

Résumé

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.

Détail

DOI : 10.2140/agt.2012.12.2299

Classification : 55M99, 57S10, 55M30, 55R91
Keywords: equivariant LS–category, equivariant sectional category, equivariant topological complexity

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