MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES

DOI10.1017/fms.2020.11zbMath1440.55007arXiv1904.01824OpenAlexW2933606305MaRDI QIDQ5221486

Christian Schlichtkrull, Fabian Hebestreit, Steffen Sagave

Publication date: 26 March 2020

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01824

zbMATH Keywords

twisted \(K\)-theorysymmetric spectraring spectraparameterized spectra

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Topological (K)-theory (55N15) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43) Twisted (K)-theory; differential (K)-theory (19L50)

Related Items (3)

Homotopical and operator algebraic twisted \(K\)-theory ⋮ A strictly commutative model for the cochain algebra of a space ⋮ Combinatorial parametrised spectra

Cites Work

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• Dwyer-Kan localization revisited
• Diagram spaces and symmetric spectra
• Day convolution for \(\infty\)-categories
• On left and right model categories and left and right Bousfield localizations
• Positive model structures for abstract symmetric spectra
• The homotopy category of parametrized spectra
• Thom spectra that are symmetric spectra
• Universality of multiplicative infinite loop space machines
• Topological Hochschild homology of Thom spectra and the free loop space
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• On topological cyclic homology
• Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map
• Units of ring spectra and their traces in algebraic K-theory
• Group completion and units in \(\mathcal I\)-spaces
• Overcategories and undercategories of cofibrantly generated model categories
• On bifibrations of model categories
• Homotopical and operator algebraic twisted \(K\)-theory
• Open maps, colimits, and a convenient category of fibre spaces
• The Grothendieck construction for model categories
• Presentably symmetric monoidal \(\infty\)-categories are represented by symmetric monoidal model categories
• On the telescopic homotopy theory of spaces
• Replacing model categories with simplicial ones
• Model Categories of Diagram Spectra
• An ∞-categorical approach to R -line bundles, R -module Thom spectra, and twisted R -homology
• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Homotopy colimits in the category of small categories
• Algebras and Modules in Monoidal Model Categories
• Symmetric spectra
• When is the Natural Map X →ΩΣX a Cofibration?
• GENERALIZED THOM SPECTRA AND THEIR TOPOLOGICAL HOCHSCHILD HOMOLOGY
• The tangent bundle of a model category
• SYMMETRIC OPERADS IN ABSTRACT SYMMETRIC SPECTRA
• Actions of $K(\pi ,n)$ spaces on $K$-theory and uniqueness of twisted $K$-theory
• Higher Topos Theory (AM-170)
• Simplicial homotopy theory
• Spectra and symmetric spectra in general model categories

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