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Group actions and higher signatures. (English) Zbl 0569.57027

Let \(M^{4k+1}\) be a simply connected closed manifold and \(\pi\) be an abelian group such that the 2-Sylow subgroup of \(\pi\) is cyclic if the semicharacteristic \(\chi_{}(M)\) is odd. Then there is a manifold \({\mathbb{Z}}_{(p)}\) equivalent to M admitting a free homologically trivial \(\pi\) action, if there is such a manifold admitting a free trivial action of the p-Sylow subgroup of \(\pi\). The author gives an outline of proofs of this result with more general studies in the nonsimply connected case related to the Novikov higher signature conjecture.
Reviewer: M.Sugawara

MSC:

57S17 Finite transformation groups
57R20 Characteristic classes and numbers in differential topology
57R19 Algebraic topology on manifolds and differential topology
57R67 Surgery obstructions, Wall groups
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