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