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Infinite loop spaces
and nilpotent K–theory
Alejandro Adem, José Manuel Gómez, John A Lind and Ulrike Tillmann |
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Algebraic & Geometric Topology 17 (2017) 869–893
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Abstract |
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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. |
Keywords
K-theory, Nilpotent K-theory
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Mathematical Subject Classification 2010
Primary: 55N15, 55R35
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References |
Publication
Received: 2 September 2015
Revised: 16 September 2016
Accepted: 29 September 2016
Published: 14 March 2017
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Authors |
| Alejandro Adem | |
| Department of Mathematics University of British Columbia 1984 Mathematics Road, Room 121 Vancouver BC V6T 1Z2 Canada |
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| José Manuel Gómez | |
| Departmento de Matemáticas Universidad Nacional de Colombia Medellín AA 3840 Colombia |
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| John A Lind | |
| Department of Mathematics Reed College 3203 SE Woodstock Blvd. Portland, OR 97202 United States |
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| Ulrike Tillmann | |
| Mathematical Institute Oxford University Oxford OX2 6GG United Kingdom |
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