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Stable Homotopy Groups of Spheres A Computer Assisted Approach

	Author(s):	Stanley O. Kochman
	Collection:
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	1990
	Language:	English
	Pages:	338 pages
	Size:	1.66 MB
	Extension:	DJVU

[tab] [content title="Description"]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. [/content] [content title="Content"] [/content] [content title="About the author"] Stanley Oscar Kochman MathSciNet Ph.D. The University of Chicago 1970 UnitedStates Dissertation: The Homology of the Classical Group over the Dyer-Lashof Algebra, a Hirsch Formula in Homology and Applications [/content] [/tab]

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