### Abstract

Original language | English |
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Publisher | ArXiv |

Number of pages | 14 |

Publication status | Submitted - 14 Aug 2019 |

### Fingerprint

### Keywords

- math.AT
- math.CT

### Cite this

*Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity*. ArXiv.

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

Research output: Working paper

}

TY - UNPB

T1 - Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity

AU - Angel, Andrés

AU - Colman, Hellen

AU - Grant, Mark

AU - Oprea, John

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.

PY - 2019/8/14

Y1 - 2019/8/14

N2 - 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.

AB - 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.

KW - math.AT

KW - math.CT

M3 - Working paper

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

PB - ArXiv

ER -