The signature of the fixed set of a map of odd period
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- by J. P. Alexander, G. C. Hamrick and J. W. Vick PDF
- Proc. Amer. Math. Soc. 57 (1976), 327-331 Request permission
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.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- 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