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arXiv · 1205.0166

Equivariant topological complexity

Hellen Colman·Mark Grant
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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 non-equivariant case. We also indicate how the equivariant topological complexity can be used to give estimates of the non-equivariant topological complexity.

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Hellen Colman, Mark Grant. 2012-05-01. Equivariant topological complexity. https://doi.org/10.2140/agt.2012.12.2299

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