Groups, Geometry, and Dynamics
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Published online: 2009-12-23
Equivariant bundles and isotropy representationsIan Hambleton and Jean-Claude Hausmann (1) McMaster University, Hamilton, Canada
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  and Goresky–Kottwitz–MacPherson .
Keywords: Equivariant bundles
Hambleton Ian, Hausmann Jean-Claude: Equivariant bundles and isotropy representations. Groups Geom. Dyn. 4 (2010), 127-162. doi: 10.4171/GGD/77