Diagram spaces, diagram spectra, and spectra of units

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 gl_1 R of a commutative ring spectrum R agree.

62 pages. The definition of the functor \mathbb{Q} is changed. Sections 8, 9, 17 and 18 contain revisions and/or new material

References in corpus (1)

• Diagram spaces and symmetric spectra

Cited by in corpus (14)

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• Symmetric spectra model global homotopy theory of finite groups
• Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces
• Orbispaces, orthogonal spaces, and the universal compact Lie group
• On the mod-$\ell$ homology of the classifying space for commutativity
• Generalized Thom spectra and their topological Hochschild homology
• Virtual vector bundles and graded Thom spectra
• G-Global Homotopy Theory and Algebraic K-Theory
• Homotopy invariance of convolution products
• Bundles of spectra and algebraic K-theory