The Lusternik-Schnirelmann category of a Lie groupoid
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Abstract:
We propose a new homotopy invariant for Lie groupoids which generalizes the classical Lusternik-Schnirelmann category for topological spaces. We use a bicategorical approach to develop a notion of contraction in this context. We propose a notion of homotopy between generalized maps given by the 2-arrows in a certain bicategory of fractions. This notion is invariant under Morita equivalence. Thus, when the groupoid defines an orbifold, we have a well-defined LS-category for orbifolds. We prove an orbifold version of the classical Lusternik-Schnirelmann theorem for critical points.References
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Additional Information
- Hellen Colman
- Affiliation: Department of Mathematics, Wilbur Wright College, 4300 N. Narragansett Avenue, Chicago, Illinois 60634
- Email: hcolman@ccc.edu
- Received by editor(s): July 21, 2008
- Received by editor(s) in revised form: July 14, 2009
- Published electronically: May 20, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 5529-5567
- MSC (2010): Primary 22A22, 55M30, 18D05
- DOI: https://doi.org/10.1090/S0002-9947-2010-05168-2
- MathSciNet review: 2657690