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

1100052514
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

169.99 In Stock
On Thom Spectra, Orientability, and Cobordism

On Thom Spectra, Orientability, and Cobordism

by Yu. B. Rudyak
On Thom Spectra, Orientability, and Cobordism

On Thom Spectra, Orientability, and Cobordism

by Yu. B. Rudyak

Overview

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

Product Details

ISBN-13: 9783540620433
Publisher: Springer Berlin Heidelberg
Publication date: 06/02/1998
Series: Springer Monographs in Mathematics
Edition description: 1998
Pages: 590
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Notation, Conventions and Other Preliminaries.- Spectra and (Co)homology Theories.- Phantoms.- Thom Spectra.- Orientability and Orientations.- K- and KO-Orientability.- Complex (Co)bordism.- (Co)bordism with Singularities.- Complex (Co)bordism with Singularities.
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