Weinberger, Shmuel Group actions and higher signatures. (English) Zbl 0569.57027 Proc. Natl. Acad. Sci. USA 82, 1297-1298 (1985). 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 Cited in 1 ReviewCited in 3 Documents 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 Keywords:free homologically trivial action; simply connected closed manifold; semicharacteristic; Novikov higher signature conjecture PDFBibTeX XMLCite \textit{S. Weinberger}, Proc. Natl. Acad. Sci. USA 82, 1297--1298 (1985; Zbl 0569.57027) Full Text: DOI