Algebraic topology--homotopy and homology
By: Robert M. Switzer.
Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete ;; Bd. 212
Publisher: Springer-Verlag
Published: 1975
Place of publication: Berlin; New York
Language: eng
Number of pages: 526
Subjects: Algebraic topology; Homotopy theory; Homology theory
Description: The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. After an account of classical homotopy theory, the author turns to homology and cohomology theories, first treating them axiomatically and then constructing them using spectra. These ideas are illustrated via a thorough development of the three main examples of ordinary homology, K-theory and bordisms. Next, the author takes up the study of products in homology and cohomology and the related questions of orientability and duality. The remainder of the book is devoted to more sophisticated techniques and methods currently in use such as characteristic classes, cohomology operations, and the Adams spectral sequence, all of which are developed in the context of generalized homology theories. This book is, all in all, a very admirable work and a valuable addition to the literature and its value is not diminished by the somewhat minor flaws mentioned. -- S.Y. Husseini.
Notes: Bibliography: p. [518]-521.
"This book is the result of lecture courses ... given by the author at the University of Manchester in 1967-1970, at Cornell University in 1970-1971, and the Georg August University, Göttingen, in 1971-72."
Includes index.