Diagram spaces, diagram spectra and spectra of units

Lind, John A

doi:10.2140/agt.2013.13.1857

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Diagram spaces, diagram spectra and spectra of units

John A Lind

Algebraic & Geometric Topology 13 (2013) 1857–1935

DOI: 10.2140/agt.2013.13.1857

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 $Ω^{\infty}$ . We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors $Ω^{\infty}$ agree. This comparison is then used to show that two different constructions of the spectrum of units ${g l}_{1} R$ 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/

Volume 13, issue 4 (2013)