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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Group completion and units in $\mathcal{I}\mkern -1mu$–spaces

Steffen Sagave and Christian Schlichtkrull

Algebraic & Geometric Topology 13 (2013) 625–686
Abstract

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 E–spaces. Working in the category of –spaces enables us to simplify and strengthen previous work on group completion and units of E–spaces. As an application we clarify the relation to Γ–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
Mathematical Subject Classification 2010
Primary: 55P48
Secondary: 55P43
References
Publication
Received: 7 February 2012
Revised: 24 September 2012
Accepted: 22 October 2012
Published: 24 March 2013
Authors
Steffen Sagave
Mathematical Institute
University of Bonn
Endenicher Allee 60
D-53115 Bonn
Germany
http://www.math.uni-bonn.de/people/sagave/
Christian Schlichtkrull
Department of Mathematics
University of Bergen
Johannes Brunsgate 12
5008 Bergen
Norway
http://www.uib.no/People/csc021/