Parametrized Homotopy Theory (Mathematical Surveys and Monographs) by J. P. May and J. Sigurdsson (PDF)

Description

This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincaré duality, transfer maps, the Adams and Wirthmüller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.

User’s Reviews

Keywords

Free Download Parametrized Homotopy Theory (Mathematical Surveys and Monographs) in PDF format
Parametrized Homotopy Theory (Mathematical Surveys and Monographs) PDF Free Download
Download Parametrized Homotopy Theory (Mathematical Surveys and Monographs) 2006 PDF Free
Parametrized Homotopy Theory (Mathematical Surveys and Monographs) 2006 PDF Free Download
Download Parametrized Homotopy Theory (Mathematical Surveys and Monographs) PDF
Free Download Ebook Parametrized Homotopy Theory (Mathematical Surveys and Monographs)