Volume 13, issue 4 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Diagram spaces, diagram spectra and spectra of units

John A Lind

Algebraic & Geometric Topology 13 (2013) 1857–1935
Abstract

This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra and EKMM S–modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor Ω. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors Ω agree. This comparison is then used to show that two different constructions of the spectrum of units gl1R of a commutative ring spectrum R agree.

Keywords
$E_\infty$–spaces, infinite loop spaces, structured ring spectra, symmetric spectra, orthogonal spectra, EKMM, spectra of units
Mathematical Subject Classification 2010
Primary: 55P42, 55P43, 55P47, 55U35, 55U40
Secondary: 55P48, 18G55
References
Publication
Received: 5 October 2009
Revised: 21 November 2012
Accepted: 20 January 2013
Published: 21 May 2013
Authors
John A Lind
Department of Mathematics
The Johns Hopkins University
3400 N. Charles St.
Baltimore, MD 21218
USA
http://math.jhu.edu/~jlind/