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Stable Homotopy Theory

Lectures delivered at the University of California at Berkeley 1961

  • Book
  • © 1964

Overview

Authors:
  1. J. Frank Adams

    1. Department of Mathematics, University of Manchester, UK

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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
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  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. Applications of Homological Algebra to Stable Homotopy Theory

    • J. Frank Adams
    Pages 38-57

  6. Theorems of periodicity and approximation in homological algebra

    • J. Frank Adams
    Pages 58-68

  7. Comments on prospective applications of 5), work in progress, etc

    • J. Frank Adams
    Pages 69-73

  8. Back Matter

    Pages 74-77
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Keywords

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.

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

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