Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 2 (2017), 869-893.
Infinite loop spaces and nilpotent K–theory
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 , , , , , and . We show that these infinite loop spaces are the zero spaces of nonunital –ring spectra. We introduce the notion of –nilpotent K–theory of a CW–complex for any , which extends the notion of commutative K–theory defined by Adem and Gómez, and show that it is represented by , where is the term of the aforementioned filtration of .
For the proof we introduce an alternative way of associating an infinite loop space to a commutative –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 –rig and show that they give rise to nonunital –ring spectra.
Algebr. Geom. Topol., Volume 17, Number 2 (2017), 869-893.
Received: 2 September 2015
Revised: 16 September 2016
Accepted: 29 September 2016
First available in Project Euclid: 19 October 2017
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Adem, Alejandro; Gómez, José; Lind, John; Tillmann, Ulrike. Infinite loop spaces and nilpotent K–theory. Algebr. Geom. Topol. 17 (2017), no. 2, 869--893. doi:10.2140/agt.2017.17.869. https://projecteuclid.org/euclid.agt/1508431447