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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Fixed points of unitary $ {\bf Z}/p\sp s$-manifolds


Authors: Stefan Waner and Yihren Wu
Journal: Proc. Amer. Math. Soc. 108 (1990), 847-853
MSC: Primary 57R85; Secondary 55P10, 57S25
MathSciNet review: 1031677
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Abstract: Let $ G = {\mathbf{Z}}/{p^s}$ ($ p$ an odd prime). We show that restricting the local representations in a unitary $ G$-manifold $ M$ with isolated fixed points results in severe restrictions on the number of fixed points (counted with the sign of their orientation), paralleling results obtained by Conner and Floyd in the case $ G = {\mathbf{Z}}/p$. Specifically, the number of noncancelling fixed points is either zero or divisible by $ {p^n}$, where $ n \to \infty $ as the dimension of $ M \to \infty $. This result also parallels phenomena in framed $ G$-manifolds, as discussed by the first author in a previous paper.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1031677-1
PII: S 0002-9939(1990)1031677-1
Article copyright: © Copyright 1990 American Mathematical Society