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Stable Homotopy Groups of Spheres: A Computer-Assisted Approach (Lecture Notes in Mathematics, 1423, Band 1423) - Softcover

Kochman, Stanley O.

 
9783540524687: Stable Homotopy Groups of Spheres: A Computer-Assisted Approach (Lecture Notes in Mathematics, 1423, Band 1423)
Softcover
ISBN 10: 3540524681 ISBN 13: 9783540524687
Verlag: Springer Berlin Heidelberg, 2008

Inhaltsangabe

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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Von der hinteren Coverseite

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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Verlag
Springer Berlin Heidelberg
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
3540524681
ISBN 13 
9783540524687
Einband
Taschenbuch
Anzahl der Seiten
344
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