Algebraic & Geometric Topology

Equivariant topological complexity

Hellen Colman and Mark Grant

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 4 (2012), 2299-2316.

Received: 2 May 2012
Revised: 2 August 2012
Accepted: 4 August 2012
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 55M99: None of the above, but in this section 57S10: Compact groups of homeomorphisms
Secondary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 55R91: Equivariant fiber spaces and bundles [See also 19L47]

equivariant LS–category equivariant sectional category equivariant topological complexity


Colman, Hellen; Grant, Mark. Equivariant topological complexity. Algebr. Geom. Topol. 12 (2012), no. 4, 2299--2316. doi:10.2140/agt.2012.12.2299.

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