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

Andrés Angel, Hellen Colman, Mark Grant, John Oprea

Research output: Working paper

### 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 ArXiv 14 Submitted - 14 Aug 2019

### Fingerprint

Lusternik-Schnirelmann Category
Topological Complexity
Equivariant
Morita Equivalence
Invariance
Invariant
Homotopy Invariance
Principal Bundle
Orbifold
Group Action
Corollary

• math.AT
• math.CT

### Cite this

Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity. / Angel, Andrés; Colman, Hellen; Grant, Mark; Oprea, John.

ArXiv, 2019.

Research output: Working paper

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N1 - This work was partially supported by grants from the Direccion de Investigacion, Desarrollo e Innovacion, Universidad del Norte (#2018-18 to Andres Angel) and the Simons Foundation (#278333 to Hellen Colman and #244393 to John Oprea). All of the authors wish to thank Wilbur Wright College, Chicago for its hospitality during the Topological Robotics Symposium in February 2018, where much of this work was carried out. The first author acknowledges and thanks the hospitality and financial support provided by the Max Planck Institute for Mathematics in Bonn where part of this paper was also carried out. We would like to thank Michael Farber, Aleksandra Franc, Wac law Marzantowicz and Yuli Rudyak for insightful discussions.

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