Ebook: On Thom Spectra, Orientability, and Cobordism

For many years, algebraic topology rests on three legs: "ordinary" cohomology, K-theory, and cobordism. This book is the first guide on the subject of cobordism since R. Stong's encyclopaedic and influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories), framed by (co)homology theories and spectra.

From the Foreword by Haynes Miller

The author has also performed a service to the history of science in this book, giving detailed attributions. This same care makes the book easy to use by the student, for when proofs are not given, specific references are.

From the reviews:

"… This is an important, formidable monograph ..... The readers interested in pursuing this line of research will find it enormously helpful to have the results assembled in one place with an unified, brilliant exposition."

Zentralblatt Math 906.1999

"This book provides an excellent and thorough treatment of various topics related to cobordism. It should become an indispensable tool for advanced graduate students and workers in algebraic topology. …"

MathSciNet MR1627486

Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's encyclopaedic and influential notes of a generation ago.

It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory, including (co)bordism with singularities.

Not only that, but Rudyak, of the University of Florida, USA, deals especially with Morava K-theories.

All of these diverse subjects are framed by (co)homology theories and spectra.

The author has also performed a service to the history of science in this book, giving detailed attributions.

This same care makes the book easy to use by the student, for when proofs are not given, specific references are.

Presented here is the second, fully corrected print run of the first edition, published in 1998, which has become a standard reference text in algebraic topology.

In sum, this is a comprehensive yet user-friendly text on a subject of high importance in the world of mathematics.

From the reviews of the first edition: "…This is an important, formidable monograph…. The readers interested in pursuing this line of research wil

Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's encyclopaedic and influential notes of a generation ago.

It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory, including (co)bordism with singularities.

Not only that, but Rudyak, of the University of Florida, USA, deals especially with Morava K-theories.

All of these diverse subjects are framed by (co)homology theories and spectra.

The author has also performed a service to the history of science in this book, giving detailed attributions.

This same care makes the book easy to use by the student, for when proofs are not given, specific references are.

Presented here is the second, fully corrected print run of the first edition, published in 1998, which has become a standard reference text in algebraic topology.

In sum, this is a comprehensive yet user-friendly text on a subject of high importance in the world of mathematics.

From the reviews of the first edition: "…This is an important, formidable monograph…. The readers interested in pursuing this line of research wil
Content:
Front Matter....Pages I-XII
Introduction....Pages 1-8
Notation, Conventions and Other Preliminaries....Pages 9-32
Spectra and (Co)homology Theories....Pages 33-133
Phantoms....Pages 135-184
Thom Spectra....Pages 185-298
Orientability and Orientations....Pages 299-338
K- and KO-Orientability....Pages 339-381
Complex (Co)bordism....Pages 383-455
(Co)bordism with Singularities....Pages 457-493
Complex (Co)bordism with Singularities....Pages 495-551
Back Matter....Pages 553-590