# Stable Homotopy Groups of Spheres

## A Computer-Assisted Approach

Part of the Lecture Notes in Mathematics book series (LNM, volume 1423)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1423)

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.

Algebraic topology Atiyah-Hirzebruch spectral sequence Homotopy Homotopy group homology homotopy theory stable stems

- DOI https://doi.org/10.1007/BFb0083795
- Copyright Information Springer-Verlag Berlin Heidelberg 1990
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-52468-7
- Online ISBN 978-3-540-46993-3
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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