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Proceedings of the American Mathematical Society

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Bordism of two commuting involutions

Author: Pedro L. Q. Pergher
Journal: Proc. Amer. Math. Soc. 126 (1998), 2141-2149
MSC (1991): Primary 57R85; Secondary 57R75
MathSciNet review: 1451825
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Abstract: In this paper we obtain conditions for a Whitney sum of three vector bundles over a closed manifold, $\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$, to be the fixed data of a $(Z_{2})^{2}$-action; these conditions yield the fact that if $(\varepsilon _{1} \oplus R) \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$ is the fixed data of a $(Z_{2})^{2}$-action, where $R \rightarrow F$ is the trivial one dimensional bundle, then the same is true for $\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$. The results obtained, together with techniques previously developed, are used to obtain, up to bordism, all possible $(Z_{2})^{2}$-actions fixing the disjoint union of an even projective space and a point.

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Pedro L. Q. Pergher
Affiliation: Universidade Federal de São Carlos, Departamento de Matemática, Rodovia Washington Luiz, km. 235, 13.565-905, São Carlos, S.P., Brazil

Keywords: $(Z_{2})^{2}$-action, fixed data, bordism class, projective space bundle, Whitney number, Smith homomorphism
Received by editor(s): November 7, 1996
Received by editor(s) in revised form: December 12, 1996
Additional Notes: The present work was partially supported by CNPq
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society