Equivariant topological complexity
Algebraic Topology
2014-10-01 v2
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.
Cite
@article{arxiv.1205.0166,
title = {Equivariant topological complexity},
author = {Hellen Colman and Mark Grant},
journal= {arXiv preprint arXiv:1205.0166},
year = {2014}
}
Comments
v1: 19 pages; v2: 14 pages. Final version, to appear in Algebraic & Geometric Topology