Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 4 (2013), 1857-1935.
Diagram spaces, diagram spectra and spectra of units
This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra and EKMM –modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor . We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors agree. This comparison is then used to show that two different constructions of the spectrum of units of a commutative ring spectrum agree.
Algebr. Geom. Topol., Volume 13, Number 4 (2013), 1857-1935.
Received: 5 October 2009
Revised: 21 November 2012
Accepted: 20 January 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55P47: Infinite loop spaces 55U35: Abstract and axiomatic homotopy theory 55U40: Topological categories, foundations of homotopy theory
Secondary: 55P48: Loop space machines, operads [See also 18D50] 18G55: Homotopical algebra
Lind, John A. Diagram spaces, diagram spectra and spectra of units. Algebr. Geom. Topol. 13 (2013), no. 4, 1857--1935. doi:10.2140/agt.2013.13.1857. https://projecteuclid.org/euclid.agt/1513715625