Involutions preserving an 𝑆𝑈 structure

Rowlett, R. J.

doi:10.1090/S0002-9947-1974-0348777-7

Involutions preserving an $\textrm {SU}$ structure
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by R. J. Rowlett

Trans. Amer. Math. Soc. 196 (1974), 137-147

DOI: https://doi.org/10.1090/S0002-9947-1974-0348777-7

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Abstract:

Bordism theories $S{U_ \ast }({Z_2},all)$ for SU-manifolds with involution and $S{U_ \ast }({Z_2},free)$ for SU-manifolds with free involution are defined. The latter is studied by use of the SU-bordism spectral sequence of $B{Z_2}$, and the orders of the spheres ${S^{4n + 3}}$ with antipodal action are determined. It is shown that $S{U_{2k}}({Z_2},free) \to S{U_{2k}}({Z_2},all)$ is monic, and that an element of $S{U_{2k}}({Z_2},all)$ bounds as a unitary involution if and only if it is a multiple of the nonzero class $\alpha \in S{U_1}$.

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