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

## TL;DR

This paper proves that certain equivariant topological invariants, including equivariant LS-category and topological complexity, remain unchanged under Morita equivalence, enabling a new way to define topological complexity for orbifolds.

## Contribution

It establishes Morita invariance of equivariant LS-category and topological complexity, extending their applicability to orbifolds.

## Key findings

- Equivariant ${
m A}$-category is Morita invariant.
- Equivariant LS-category is invariant under Morita equivalence.
- Invariant topological complexity is Morita invariant.

## 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.