Proper actions on rational cohomology manifolds
by
Harald Biller
Technische Universität Darmstadt

Some essential results about actions of compact Lie groups on manifolds are generalized to proper actions (of arbitrary groups) on rational cohomology manifolds. The group dimension is shown to be effectively finite. The orbits of maximal dimension are described. This corresponds to work by Yang. It allows to generalize a criterion due to Bredon for the group to be a Lie group. For actions of compact connected abelian groups on (rational cohomology) spheres, we prove the analogues of Smith's fixed point theorems and of Borel's sum formula, which yields a sharp upper bound for the group dimension.

Date received: February 28, 2001