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Brown-Peterson Homology: An Introduction and Sampler
W. Stephen Wilson
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1982; 86 pp; softcover
Number: 48
Reprint/Revision History:
reprinted 2005
ISBN-10: 0-8218-1699-3
ISBN-13: 978-0-8218-1699-8
List Price: US$22
Member Price: US$17.60
All Individuals: US$17.60
Order Code: CBMS/48
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This book is primarily directed to graduate students interested in the field and to algebraic topologists who wish to learn something about BP. Beginning with the geometric background of complex bordism, the author goes on to a discussion of formal groups and an introduction to BP-homology. He then presents his view of the major developments in the field in the last decade (the calculation of the homology of Eilenberg-MacLane spaces in this section may be useful in teaching advanced algebraic topology courses). The book concludes with a section on unstable operations with comments on where applications may come from in the future.

Readership

Reviews

"An excellent book ... very useful [to] students and others wanting to learn BP-homology theory."

-- Franklin P. Peterson, Mathematical Reviews

Table of Contents

  • Part 1. An introduction
  • Complex bordism
  • Formal groups
  • Brown-Peterson homology
  • Part II. A sampler
  • Cooperations and stable homotopy
  • Associated homology theories
  • Morava's little structure theorem and the Conner-Floyd conjecture
  • Hopf rings, the bar spectral sequence, and \(K(n)_*\underline K_*\)
  • \(H_*\underline K_*\) and the Steenrod algebra
  • Two formal groups and \(BP_*\underline{BP}_*\)
  • Chan's proof of no torsion in \(H_*\underline{BP}_*\)
  • Part III. Something new
  • Unstable operations
  • References
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