This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas-de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classesand include some applications to homotopy theory. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, Differential Forms in Algebraic Topology should be suitable for self-study or for a one-semester course in topology.
TAILLE DU FICHIER: 4,47 MB
DATE DE PUBLICATION: 1982-Jan-01
AUTEUR: Raoul Bott
NOM DE FICHIER: Differential Forms in Algebraic Topology.pdf
The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accord ingly, we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to
"Bott and Tu give us an introduction to algebraic topology via differential forms, imbued with the spirit of a master who knew differential forms way back when, yet written from a mature point of view which draws together the separate paths traversed by de Rham theory and homotopy theory.