Group actions and higher signatures

Abstract

Let π be a nontrivial finite group and M be a closed manifold. An interesting question is whether or not M has the R-homology type of a manifold admitting a free π action. Here this problem is studied for actions that are “homologically trivial.” If π₁ M is nontrivial these questions are intimately related to the Novikov higher signature conjecture, but the results are new even in the simply connected case.

• transformation groups
• surgery theory
• Novikov's conjectures