Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory
Benjamin Antieau, David Gepner, Jos\'e Manuel G\'omez
TL;DR
This paper proves the uniqueness of twisted K-theory for real and complex cases by leveraging the K-theories of Eilenberg-MacLane spaces, and explores actions of these spaces on K-theory spectra.
Contribution
It introduces a novel proof of the uniqueness of twisted K-theory using classical K-theory computations of Eilenberg-MacLane spaces.
Findings
Established the uniqueness of twisted K-theory in real and complex cases.
Provided vanishing results for actions of Eilenberg-MacLane spaces on K-theory spectra.
Applied classical K-theory computations to modern problems in twisted K-theory.
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Ophthalmology and Eye Disorders