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Group completion and
units in $\mathcal{I}\mkern -1mu$–spaces
Steffen Sagave and Christian Schlichtkrull |
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Algebraic & Geometric Topology 13 (2013) 625–686
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Abstract |
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The category of –spaces is the diagram category of spaces indexed by finite sets and injections. This is a symmetric monoidal category whose commutative monoids model all –spaces. Working in the category of –spaces enables us to simplify and strengthen previous work on group completion and units of –spaces. As an application we clarify the relation to –spaces and show how the spectrum of units associated with a commutative symmetric ring spectrum arises through a chain of Quillen adjunctions. |
Keywords
$E_{\infty}$–spaces, group completion, units of ring
spectra, $\Gamma$–spaces
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Mathematical Subject Classification 2010
Primary: 55P48
Secondary: 55P43
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References |
Publication
Received: 7 February 2012
Revised: 24 September 2012
Accepted: 22 October 2012
Published: 24 March 2013
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Authors |
| Steffen Sagave | |
| Mathematical Institute University of Bonn Endenicher Allee 60 D-53115 Bonn Germany |
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| http://www.math.uni-bonn.de/people/sagave/ | |
| Christian Schlichtkrull | |
| Department of Mathematics University of Bergen Johannes Brunsgate 12 5008 Bergen Norway |
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| http://www.uib.no/People/csc021/ | |
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