Orbifolds and stable homotopy groups

Details Orbifolds and stable homotopy groups Orbifolds and stable homotopy groups

2005-05-20

arxiv.org/abs/math/0505431v1

Mathematics

Algebraic Topology

16 pages, no figures

Scientific paper

Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy theory using such groupoids. A different sort of twisted sector, along with a classical theorem of tom Dieck, allows for a natural definition of stable orbifold homotopy groups, and motivates defining extended unstable orbifold homotopy groups generalizing previous definitions.

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