Local Homotopy Theory

• Main Author: Jardine, John F. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2015.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Category theory (Mathematics).; Homological algebra.; K-theory.; Algebraic topology.; Category Theory, Homological Algebra.; K-Theory.; Algebraic Topology.

This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simpli...

Table of Contents:

• Preface
• 1 Introduction
• Part I Preliminaries
• 2 Homotopy theory of simplicial sets
• 3 Some topos theory
• Part II Simplicial presheaves and simplicial sheaves
• 4 Local weak equivalences
• 5 Local model structures
• 6 Cocycles
• 7 Localization theories
• Part III Sheaf cohomology theory
• 8 Homology sheaves and cohomology groups
• 9 Non-abelian cohomology
• Part IV Stable homotopy theory
• 10 Spectra and T-spectra
• 11 Symmetric T-spectra
• References
• Index.