Morita invariance of equivariant Lusternik-Schnirelmann category and invariant topological complexity

A. Angel, H. Colman, M. Grant and J. Oprea

We use the homotopy invariance of equivariant principal bundles to prove that the equivariant A-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds.

Keywords: Topological complexity, Lusternik-Schnirelmann category

2010 MSC: 55M30, 55R91

Theory and Applications of Categories, Vol. 35, 2020, No. 7, pp 179-195.

Published 2020-02-18.

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