Orbifolds and stable homotopy groups

2005/05/20 by Johann K. Leida, Leida, Johann K.
Mathematics · #22A22 (Secondary) #55P91 (Primary) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:22A22 #msc:55P91

paper · pdf · doi:10.48550/arxiv.math/0505431

16 pages, no figures

arxiv created 2005/05/20 · arxiv updated 2009/12/01

Abstract

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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