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Parametrized Homotopy Theory Volume 132 by May, J. Peter; Sigurdsson, J. is a nonfiction available to read on EtoBox.

What is Parametrized Homotopy Theory Volume 132 about?

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 dev

Who reads Parametrized Homotopy Theory Volume 132?

Author

May, J. Peter; Sigurdsson, J.

Publisher

American Mathematical Society

Published

2006

Language

EN

ISBN

9780821839225

Category

nonfiction

Subjects

Mathematics, Stem