Group completion and units in I-spaces

Abstract

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-infinity spaces. Working in the category of I-spaces enables us to simplify and strengthen previous work on group completion and units of E-infinity spaces. As an application we clarify the relation to Gamma-spaces and show how the spectrum of units associated with a commutative symmetric ring spectrum arises through a chain of Quillen adjunctions.

v3: 43 pages. Minor revisions, accepted for publication in Algebraic and Geometric Topology

References in corpus (1)

• Units of ring spectra and Thom spectra

Cited by in corpus (14)

• Localization sequences for logarithmic topological Hochschild homology
• Logarithmic structures on topological K-theory spectra
• Symmetric spectra model global homotopy theory of finite groups
• Twisted Spin cobordism and positive scalar curvature
• Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces
• Topological Hochschild homology and the cyclic bar construction in symmetric spectra
• Derived Logarithmic Geometry I
• $K$-theory of Hermitian Mackey functors and a reformulation of the Novikov Conjecture
• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Homotopical and operator algebraic twisted K-theory
• Equivariant stable categories for incomplete systems of transfers
• Generalized Thom spectra and their topological Hochschild homology
• Virtual vector bundles and graded Thom spectra
• Exponential Functors, R-Matrices and Twists