Bordism of two commuting involutions

Pergher, Pedro

doi:10.1090/S0002-9939-98-04356-1

Bordism of two commuting involutions
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by Pedro L. Q. Pergher

Proc. Amer. Math. Soc. 126 (1998), 2141-2149

DOI: https://doi.org/10.1090/S0002-9939-98-04356-1

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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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