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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The signature of the fixed set of a map of odd period


Authors: J. P. Alexander, G. C. Hamrick and J. W. Vick
Journal: Proc. Amer. Math. Soc. 57 (1976), 327-331
MSC: Primary 57D85
DOI: https://doi.org/10.1090/S0002-9939-1976-0407862-9
MathSciNet review: 0407862
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Abstract: Let $ T$ be a diffeomorphism of odd period $ n$ on a closed smooth manifold $ {M^{2k}}$. The Conner-Floyd analysis of fixed point data and the Atiyah-Singer Index Theorem are applied to prove there exist methods of orienting the components $ F$ of the fixed set of $ T$, depending only on $ n$, so that $ {\Sigma _F}\operatorname{sgn} F \equiv \operatorname{sgn} M\bmod 4$ whenever $ {T^ \ast }$ is the identity on $ {H^k}(M;Q)$. Other special results of this type are obtained when assumptions are made restricting the possible eigenvalues in the normal bundle to the fixed set.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0407862-9
Article copyright: © Copyright 1976 American Mathematical Society