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Orbifolds and stable homotopy groups

Johann K. Leida
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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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Johann K. Leida. 2005-05-20. Orbifolds and stable homotopy groups. https://arxiv.org/abs/math/0505431

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