The Lusternik-Schnirelmann category of a Lie groupoid

Colman, Hellen

doi:10.1090/S0002-9947-2010-05168-2

The Lusternik-Schnirelmann category of a Lie groupoid
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Trans. Amer. Math. Soc. 362 (2010), 5529-5567 Request permission

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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