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English

Equivariant Bundles and Isotropy Representations

Published inGroups, geometry, and dynamics, vol. 4, no. 1, p. 127-162
Publication date2010
Abstract

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinatorial classification of bundles with structural group G a compact connected Lie group. If G is abelian, our approach gives combinatorial and geometric descriptions of some results of Lashof-May-Segal [18] and Goresky-Kottwitz-MacPherson [10].

Classification
  • arxiv : math.GT
NoteFinal version: to appear in "Groups, Geometry and Dynamics"
Citation (ISO format)
HAMBLETON, Ian, HAUSMANN, Jean-Claude. Equivariant Bundles and Isotropy Representations. In: Groups, geometry, and dynamics, 2010, vol. 4, n° 1, p. 127–162. doi: 10.4171/ggd/77
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ISSN of the journal1661-7207
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Creation09/21/2010 11:38:00 AM
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