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2017 Infinite loop spaces and nilpotent K–theory
Alejandro Adem, José Gómez, John Lind, Ulrike Tillmann
Algebr. Geom. Topol. 17(2): 869-893 (2017). DOI: 10.2140/agt.2017.17.869

Abstract

Using a construction derived from the descending central series of the free groups, we produce filtrations by infinite loop spaces of the classical infinite loop spaces BSU, BU, BSO, BO, BSp, BGL(R)+ and Q0(S0). We show that these infinite loop spaces are the zero spaces of nonunital E–ring spectra. We introduce the notion of q–nilpotent K–theory of a CW–complex X for any q 2, which extends the notion of commutative K–theory defined by Adem and Gómez, and show that it is represented by × B(q,U), where B(q,U) is the qth term of the aforementioned filtration of BU.

For the proof we introduce an alternative way of associating an infinite loop space to a commutative I–monoid and give criteria for when it can be identified with the plus construction on the associated limit space. Furthermore, we introduce the notion of a commutative I–rig and show that they give rise to nonunital E–ring spectra.

Citation

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Alejandro Adem. José Gómez. John Lind. Ulrike Tillmann. "Infinite loop spaces and nilpotent K–theory." Algebr. Geom. Topol. 17 (2) 869 - 893, 2017. https://doi.org/10.2140/agt.2017.17.869

Information

Received: 2 September 2015; Revised: 16 September 2016; Accepted: 29 September 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1360.55003
MathSciNet: MR3623675
Digital Object Identifier: 10.2140/agt.2017.17.869

Subjects:
Primary: 55N15, 55R35

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 2 • 2017
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