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Real K-theories

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Abstract

The purpose of this short paper is to investigate relations between various real K-theories. In particular, we show how a real projective bundle theorem implies an unexpected relation between Atiyah’s K R-theory and the usual equivariant K-theory of real vector bundles. This relation has been used recently in a new computation of the Witt group of real curves [10], Section 4. We also interpret Atiyah’s theory as a special case of twisted K-theory.

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Authors and Affiliations

  1. UFR de mathématiques, Université Paris 7-Denis Diderot, 75013, Paris, France

    Max Karoubi

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  1. Max Karoubi
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Correspondence to Max Karoubi.

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Karoubi, M. Real K-theories. Isr. J. Math. 253, 91–99 (2023). https://doi.org/10.1007/s11856-022-2356-9

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  • DOI: https://doi.org/10.1007/s11856-022-2356-9

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