# 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 179-195 14 Theory and Applications of Categories 35 7 Published - 18 Feb 2020

### Keywords

• math.AT
• math.CT
• Lusternik-Schnirelmann category
• Topological complexity