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Stable Homotopy Groups of Spheres

A Computer-Assisted Approach

  • Book
  • © 1990

Overview

Authors:
  1. Stanley O. Kochman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1423)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Stanley O. Kochman
    Pages 1-11

  3. Toda brackets

    • Stanley O. Kochman
    Pages 12-34

  4. Low dimensional computations

    • Stanley O. Kochman
    Pages 35-71

  5. The image of J

    • Stanley O. Kochman
    Pages 72-98

  6. The Japanese stems (πN, 9≤N≤31)

    • Stanley O. Kochman
    Pages 99-138

  7. The Chicago stem (πS N, 32≤N≤45)

    • Stanley O. Kochman
    Pages 139-211

  8. The new stems (πS N, 46≤N≤64)

    • Stanley O. Kochman
    Pages 212-283

  9. The elements of arf invariant one

    • Stanley O. Kochman
    Pages 284-293

  10. Back Matter

    Pages 294-330
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Keywords

About this book

A central problem in algebraic topology is the calculation of the values of the stable homotopy groups of spheres +*S. In this book, a new method for this is developed based upon the analysis of the Atiyah-Hirzebruch spectral sequence. After the tools for this analysis are developed, these methods are applied to compute inductively the first 64 stable stems, a substantial improvement over the previously known 45. Much of this computation is algorithmic and is done by computer. As an application, an element of degree 62 of Kervaire invariant one is shown to have order two. This book will be useful to algebraic topologists and graduate students with a knowledge of basic homotopy theory and Brown-Peterson homology; for its methods, as a reference on the structure of the first 64 stable stems and for the tables depicting the behavior of the Atiyah-Hirzebruch and classical Adams spectral sequences through degree 64.

Bibliographic Information

  • Book Title: Stable Homotopy Groups of Spheres

  • Book Subtitle: A Computer-Assisted Approach

  • Authors: Stanley O. Kochman

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0083795

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52468-7Published: 04 April 1990

  • eBook ISBN: 978-3-540-46993-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 334

  • Topics: Algebraic Topology, Algorithm Analysis and Problem Complexity

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