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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Involutions preserving an $ {\rm SU}$ structure


Author: R. J. Rowlett
Journal: Trans. Amer. Math. Soc. 196 (1974), 137-147
MSC: Primary 57D85
DOI: https://doi.org/10.1090/S0002-9947-1974-0348777-7
MathSciNet review: 0348777
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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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DOI: https://doi.org/10.1090/S0002-9947-1974-0348777-7
Keywords: Involution, SU-manifold, Wall manifold
Article copyright: © Copyright 1974 American Mathematical Society