A $W(Z_{2})$ invariant for orientation preserving involutions
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- by John P. Alexander PDF
- Proc. Amer. Math. Soc. 51 (1975), 455-460 Request permission
Abstract:
In this paper we calculate an invariant in $W({{\mathbf {Z}}_2})$, the Witt ring of nonsingular, symmetric ${{\mathbf {Z}}_2}$-inner product spaces, for orientation-preserving involutions on compact, closed, connected $4n$-dimensional manifolds $M$. This invariant with the Atiyah-Singer index theorem uniquely determines the orthogonal representation of ${{\mathbf {Z}}_2}$ on ${H^{2n}}(M;{\mathbf {Z}})/\operatorname {TOR}$. We also give an example to show that this invariant detects actions that the Atiyah-Singer theorem cannot.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 51 (1975), 455-460
- MSC: Primary 57E15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377947-3
- MathSciNet review: 0377947