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

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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.

http://www.tac.mta.ca/tac/volumes/35/7/35-07.pdf

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