JournalsggdVol. 4, No. 1pp. 127–162

Equivariant bundles and isotropy representations

  • Ian Hambleton

    McMaster University, Hamilton, Canada
  • Jean-Claude Hausmann

    Université de Genève, Switzerland
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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].

Cite this article

Ian Hambleton, Jean-Claude Hausmann, Equivariant bundles and isotropy representations. Groups Geom. Dyn. 4 (2010), no. 1, pp. 127–162

DOI 10.4171/GGD/77