Group actions and higher signatures.
Let pi 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 pi action. Here this problem is studied for actions that are "homologically trivial." If pi(1)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.
Department of Mathematics, Princeton University, Princeton, NJ 08544.
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Weinberger