The Lusternik-Schnirelmann category of a Lie groupoid
Algebraic Topology
2009-08-25 v1 Category Theory
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.
Keywords
Cite
@article{arxiv.0908.3325,
title = {The Lusternik-Schnirelmann category of a Lie groupoid},
author = {Hellen Colman},
journal= {arXiv preprint arXiv:0908.3325},
year = {2009}
}