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  • © 1964

Stable Homotopy Theory

Lectures delivered at the University of California at Berkeley 1961

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 3)

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Table of contents (6 chapters)

  1. Front Matter

    Pages N2-iii
  2. Introduction

    • J. Frank Adams
    Pages 1-3
  3. Primary operations

    • J. Frank Adams
    Pages 4-21
  4. Stable Homotopy Theory

    • J. Frank Adams
    Pages 22-37
  5. Back Matter

    Pages 74-77

About this book

Before I get down to the business of exposition, I'd like to offer a little motivation. I want to show that there are one or two places in homotopy theory where we strongly suspect that there is something systematic going on, but where we are not yet sure what the system is. The first question concerns the stable J-homomorphism. I recall that this is a homomorphism J: ~ (SQ) ~ ~S = ~ + (Sn), n large. r r r n It is of interest to the differential topologists. Since Bott, we know that ~ (SO) is periodic with period 8: r 6 8 r = 1 2 3 4 5 7 9· . · Z o o o z On the other hand, ~S is not known, but we can nevertheless r ask about the behavior of J. The differential topologists prove: 2 Th~~: If I' = ~ - 1, so that 'IT"r(SO) ~ 2, then J('IT"r(SO)) = 2m where m is a multiple of the denominator of ~/4k th (l\. being in the Pc Bepnoulli numher.) Conject~~: The above result is best possible, i.e. J('IT"r(SO)) = 2m where m 1s exactly this denominator. status of conJectuI'e ~ No proof in sight. Q9njecture Eo If I' = 8k or 8k + 1, so that 'IT"r(SO) = Z2' then J('IT"r(SO)) = 2 , 2 status of conjecture: Probably provable, but this is work in progl'ess.

Keywords

  • Division
  • Homological algebra
  • Homotopie
  • Homotopy
  • Morphism
  • behavior
  • homomorphism
  • homotopy theory
  • proof
  • system

Authors and Affiliations

  • Department of Mathematics, University of Manchester, UK

    J. Frank Adams

Bibliographic Information

  • Book Title: Stable Homotopy Theory

  • Book Subtitle: Lectures delivered at the University of California at Berkeley 1961

  • Authors: J. Frank Adams

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-15942-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1964

  • eBook ISBN: 978-3-662-15942-2Published: 11 November 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: III, 77

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Topology

Buying options

eBook USD 44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions