Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
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 ku–group ring of BU(1) and thus obtain a splitting of its representing space BcomU as a product of all the terms in the Whitehead tower for BU, BcomU ≃ BU × BU〈4〉× BU〈6〉×⋯. As a consequence of the spectrum level identification we obtain the ring of coefficients for this theory. Using the rational Hopf ring for BcomU we describe the relationship of our results with a previous computation of the rational cohomology algebra of BcomU. This gives an essentially complete description of the space BcomU introduced by A Adem and J Gómez.
Keywords: $K$–theory, classifying space
Gritschacher, Simon 1
@article{10_2140_agt_2018_18_1205,
author = {Gritschacher, Simon},
title = {The spectrum for commutative complex {K{\textendash}theory}},
journal = {Algebraic and Geometric Topology},
pages = {1205--1249},
publisher = {mathdoc},
volume = {18},
number = {2},
year = {2018},
doi = {10.2140/agt.2018.18.1205},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.1205/}
}
TY - JOUR AU - Gritschacher, Simon TI - The spectrum for commutative complex K–theory JO - Algebraic and Geometric Topology PY - 2018 SP - 1205 EP - 1249 VL - 18 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.1205/ DO - 10.2140/agt.2018.18.1205 ID - 10_2140_agt_2018_18_1205 ER -
Gritschacher, Simon. The spectrum for commutative complex K–theory. Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 1205-1249. doi: 10.2140/agt.2018.18.1205
Cité par Sources :