Cosimplicial resolutions and homotopy spectral sequences in model categories

DOI10.2140/gt.2003.7.1001zbMath1065.55012arXivmath/0312531OpenAlexW3098141038MaRDI QIDQ1774808

A. K. Bousfield

Publication date: 19 May 2005

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312531

zbMATH Keywords

model categoriesBousfield-Kan completionhomotopy spectral sequencesBendersky-Thompson completionCosimplicial resolutions

Mathematics Subject Classification ID

Localization and completion in homotopy theory (55P60) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Adams spectral sequences (55T15)

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Cites Work

• The localization of spectra with respect to homology
• Homologie nicht-additiver Funktoren. Anwendungen
• Homotopy spectral sequences and obstructions
• The localization of spaces with respect to homology
• An arithmetic square for virtually nilpotent spaces
• Localization with respect to K-theory
• The unstable Adams spectral sequence for generalized homology
• The \(K\)-theory localizations and \(v_1\)-periodic homotopy groups of H-spaces
• An \(E^ 2\) model category structure for pointed simplicial spaces
• A stable approach to an unstable homotopy spectral sequence.
• Cosimplicial resolutions and homotopy spectral sequences in model categories
• Universal spaces for homotopy limits of modules over coaugmented functors. II
• Homotopy limits of triples
• On \(\lambda\)-rings and the \(K\)-theory of infinite loop spaces
• Homotopical algebra
• The homotopy spectral sequence of a space with coefficients in a ring
• Steenrod operations in the Eilenberg-Moore spectral sequence
• The core of a ring
• Homotopy limits, completions and localizations
• On the telescopic homotopy theory of spaces
• The Bousfield-Kan spectral sequence for periodic homology theories
• ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM
• Symmetric spectra
• Cosimplicial Homotopies
• Pairings and Products in the Homotopy Spectral Sequence
• Compositions in the ν1 -periodic homotopy groups of spheres
• Foundations of relative homological algebra
• Simplicial homotopy theory
• On \(p\)-adic \(\lambda\)-rings and the \(K\)-theory of \(H\)-spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item