Actions of 𝐾(𝜋,𝑛) spaces on 𝐾-theory and uniqueness of twisted 𝐾-theory

Antieau, Benjamin; Gepner, David; Gómez, José

doi:10.1090/S0002-9947-2014-05937-0

Actions of $K(\pi ,n)$ spaces on $K$-theory and uniqueness of twisted $K$-theory
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Abstract:

We prove the uniqueness of twisted $K$-theory in both the real and complex cases using the computation of the $K$-theories of Eilenberg-MacLane spaces due to Anderson and Hodgkin. As an application of our method, we give some vanishing results for actions of Eilenberg-MacLane spaces on $K$-theory spectra.

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