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].
1
McMaster University, Hamilton, Canada
2
Université de Genève, Switzerland
Ian Hambleton; Jean-Claude Hausmann. Equivariant bundles and isotropy representations. Groups, geometry, and dynamics, Tome 4 (2010) no. 1, pp. 127-162. doi: 10.4171/ggd/77
@article{10_4171_ggd_77,
author = {Ian Hambleton and Jean-Claude Hausmann},
title = {Equivariant bundles and isotropy representations},
journal = {Groups, geometry, and dynamics},
pages = {127--162},
year = {2010},
volume = {4},
number = {1},
doi = {10.4171/ggd/77},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/77/}
}
TY - JOUR
AU - Ian Hambleton
AU - Jean-Claude Hausmann
TI - Equivariant bundles and isotropy representations
JO - Groups, geometry, and dynamics
PY - 2010
SP - 127
EP - 162
VL - 4
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/77/
DO - 10.4171/ggd/77
ID - 10_4171_ggd_77
ER -
