Equivariant topological complexity

Hellen Colman*, Mark Grant

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2299-2316
Number of pages18
JournalAlgebraic & Geometric Topology
Volume12
Issue number4
DOIs
Publication statusPublished - 8 Jan 2013

Keywords

  • Lusternik-Schnirelmann category
  • robot motion
  • category
  • equivariant LS-category
  • equivariant sectional category
  • equivariant topological complexity

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