# Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity

Andrés Angel* (Corresponding Author), Hellen Colman, Mark Grant, John Oprea

*Corresponding author for this work

Research output: Contribution to journalArticle

### Abstract

We use the homotopy invariance of equivariant principal bundles to prove that the equivariant ${\mathcal A}$-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.
Original language English 14 Theory and Applications of Categories Accepted/In press - 11 Feb 2020

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