Orbit configuration spaces and equivariant loop spaces.
by
Miguel A. Xicoténcatl
CINVESTAV, Mexico City

Given a manifold M with a G-action, we analyze an equivariant version of the ordinary configuration spaces of Fadell and Neuwirth. After deriving their basic properties, we look at the homology and loop space homology of some examples, which turn out to be hyperplane arrangements. An interesting fact is the appearence of equivariant ``infinitesimal pure braid relations'' and an extra relation in the description of the latter.

Secondly, we show how to use theses spaces to construct a combinatorial model for the space of equivariant loop of a space X, which we use it to give an splitting of (\Omegaⁿ \Sigmaⁿ X)^Z₂ for a well pointed Z₂-space X. These methods can also be adapted to study (\Omegaⁿ \Sigmaⁿ X)^G for a finite group G.

Date received: June 3, 1999