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 |
|---|---|
| Pages (from-to) | 179-195 |
| Number of pages | 14 |
| Journal | Theory and Applications of Categories |
| Volume | 35 |
| Issue number | 7 |
| Publication status | Published - 18 Feb 2020 |
Bibliographical note
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.
Keywords
- math.AT
- math.CT
- Lusternik-Schnirelmann category
- Topological complexity