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


Authors: Benjamin Antieau, David Gepner and José Manuel Gómez
Journal: Trans. Amer. Math. Soc. 366 (2014), 3631-3648
MSC (2010): Primary 19L50, 55N15
DOI: https://doi.org/10.1090/S0002-9947-2014-05937-0
Published electronically: March 14, 2014
MathSciNet review: 3192610
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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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Additional Information

Benjamin Antieau
Affiliation: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
Address at time of publication: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: antieau@math.ucla.edu, benjamin.antieau@gmail.com

David Gepner
Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Address at time of publication: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
Email: djgepner@gmail.com, djgepner@gmail.com

José Manuel Gómez
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Address at time of publication: Departmento de Matemáticas, Universidad Nacional de Colombia, Medellín, AA 3840 Colombia
Email: jgomez@math.jhu.edu, jmgomez0@unal.edu.co

DOI: https://doi.org/10.1090/S0002-9947-2014-05937-0
Keywords: Twisted $K$-theory, units of ring spectra, topological Brauer groups
Received by editor(s): October 13, 2011
Received by editor(s) in revised form: August 16, 2012
Published electronically: March 14, 2014
Additional Notes: The first author was supported in part by the NSF under Grant RTG DMS 0838697
Article copyright: © Copyright 2014 American Mathematical Society