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.

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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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Table of contents (8 chapters)

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