Equivariant Bundles and Isotropy Representations

Details Equivariant Bundles and Isotropy Representations Equivariant Bundles and Isotropy Representations

2007-04-20

arxiv.org/abs/0704.2763v2

Mathematics

Geometric Topology

Final version: to appear in "Groups, Geometry and Dynamics"

Scientific paper

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex $A=\Gamma\backslash X$ is a graph, with all edge stabilizers toral subgroups of $\Gamma$, 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.

Affiliated with

Also associated with

No associations

Rating

Equivariant Bundles and Isotropy Representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivariant Bundles and Isotropy Representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivariant Bundles and Isotropy Representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-573988