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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Lusternik-Schnirelmann category of a Lie groupoid


Author: Hellen Colman
Journal: Trans. Amer. Math. Soc. 362 (2010), 5529-5567
MSC (2010): Primary 22A22, 55M30, 18D05
Published electronically: May 20, 2010
MathSciNet review: 2657690
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05168-2
PII: S 0002-9947(2010)05168-2
Received by editor(s): July 21, 2008
Received by editor(s) in revised form: July 14, 2009
Published electronically: May 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.