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Bordism, Stable Homotopy and Adams Spectral Sequences
Stanley O. Kochman, York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Monographs
1996; 272 pp; hardcover
Volume: 7
ISBN-10: 0-8218-0600-9
ISBN-13: 978-0-8218-0600-5
List Price: US$60
Member Price: US$48
Order Code: FIM/7
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This book is a compilation of lecture notes that were prepared for the graduate course "Adams Spectral Sequences and Stable Homotopy Theory" given at The Fields Institute during the fall of 1995. The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems.

Suitable as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism, characteristic classes, Adams spectral sequences, Brown-Peterson spectra and the computation of stable stems. The key ideas are presented in complete detail without becoming encyclopedic. The approach to characteristic classes and some of the methods for computing stable stems have not been published previously.

  • All results are proved in complete detail.
  • Only elementary facts from algebraic topology and homological algebra are assumed.
  • Each chapter concludes with a guide for further study.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students, research mathematicians, and theoretical physicists interested in algebraic topology.

Reviews

"The contents of Kochman's book look promising to the would-be student, with five well-balanced chapters augmented by sections on further reading ... clearly self-contained ... beautifully produced."

-- Bulletin of the London Mathematical Society

Table of Contents

  • Bordism
  • Characteristic classes
  • Stable category
  • Complex bordism
  • Computing stable stems
  • Bibliography
  • Index
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