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Field name	Details
Dewey Class	512.2
Title	Syzygies and Homotopy Theory ([Ebook]) / by F.E.A. Johnson.
Author	Johnson, F. E. A. (Francis Edward Anthony) , 1946-
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2012.
Physical Details	XXIV, 294 pages: 1 illus. : online resource.
Series	Algebra and Applications 1572-5553 ; ; 17
ISBN	9781447122944
Summary Note	The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn Â´F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.:
Contents note	Preliminaries -- The restricted linear group -- The calculus of corners and squares -- Extensions of modules -- The derived module category -- Finiteness conditions -- The Swan mapping -- Classification of algebraic complexes -- Rings with stably free cancellation -- Group rings of cyclic groups -- Group rings of dihedral groups -- Group rings of quaternionic groups -- Parametrizing W1 (Z) : generic case -- Parametrizing W1 (Z) : singular case -- Generalized Swan modules -- Parametrizing W1 (Z) : G = CÂ¥ Â´ F -- Conclusion .
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-2294-4
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Authors: Johnson, F. E. A. (Francis Edward Anthony) 1946- . Corporate Authors: SpringerLink (Online service) . Series: Algebra and Applications . Classification: 512.2 . 512.2 (DDC 23) .

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Syzygies and Homotopy Theory

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