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2018 The spectrum for commutative complex $K$–theory
Simon Philipp Gritschacher
Algebr. Geom. Topol. 18(2): 1205-1249 (2018). DOI: 10.2140/agt.2018.18.1205

Abstract

We study commutative complex K –theory, a generalised cohomology theory built from spaces of ordered commuting tuples in the unitary groups. We show that the spectrum for commutative complex K –theory is stably equivalent to the k u –group ring of B U ( 1 ) and thus obtain a splitting of its representing space B com U as a product of all the terms in the Whitehead tower for B U , B com U B U × B U 4 × B U 6 × . As a consequence of the spectrum level identification we obtain the ring of coefficients for this theory. Using the rational Hopf ring for B com U we describe the relationship of our results with a previous computation of the rational cohomology algebra of  B com U . This gives an essentially complete description of the space B com U introduced by A Adem and J Gómez.

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Simon Philipp Gritschacher. "The spectrum for commutative complex $K$–theory." Algebr. Geom. Topol. 18 (2) 1205 - 1249, 2018. https://doi.org/10.2140/agt.2018.18.1205

Information

Received: 14 September 2017; Revised: 24 November 2017; Accepted: 16 December 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859619
MathSciNet: MR3773753
Digital Object Identifier: 10.2140/agt.2018.18.1205

Subjects:
Primary: 55N15
Secondary: 55R35, 55R40, 55R50

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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