On the cohomology of orbit configuration spaces of spheres
by
Eva Maria Feichtner
Institute for Advanced Study, Princeton
Coauthors: Günter M. Ziegler (TU Berlin)

We consider spaces of point configurations on spheres, where points are required to be pairwise distinct and non-antipodal. These spaces are basic instances of so-called orbit configuration spaces that have recently attracted interest in the study of equivariant function spaces.

We focus on determining the integer cohomology algebras of the orbit configuration spaces of spheres described above. The topological theory of hyperplane arrangements and of subspace arrangements turned out to be essential for determining cohomology of classical ordered configuration spaces of spheres, as we have shown in earlier work. We review these results and discuss the extension of our approach to orbit configuration spaces. Again, complements of subspace arrangements figure prominently, though in a less direct way. We are left with an interesting investigation on the borderline of linear and non-linear structure.

http://www.math.ias.edu/~feichtne

Date received: May 31, 1999