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

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Angel,  A.
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Angel, A., Colman, H., Grant, M., & Oprea, J. (2020). Morita invariance of equivariant Lusternik-Schnirelmann category and invariant topological complexity. Theory and Applications of Categories, 35(7), 179-195.

Cite as: http://hdl.handle.net/21.11116/0000-0007-D98E-5
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.