Group completion and units in I-spaces

Sagave, Steffen¹ ; Schlichtkrull, Christian²

¹Mathematical Institute, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
²Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway

Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 625-686

Résumé

The category of ℐ–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 ℐ–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.

Détail

DOI : 10.2140/agt.2013.13.625

Classification : 55P48, 55P43
Keywords: $E_{\infty}$–spaces, group completion, units of ring spectra, $\Gamma$–spaces

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