000			03603nam a22003735i 4500
001			287267
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007			cr nn 008mamaa
008			150903s2012 xxk| o |||| 0|eng d
020			_a9781447122944 _99781447122944
024	7		_a10.1007/9781447122944 _2doi
035			_avtls000339546
039		9	_a201509030839 _bVLOAD _c201404300401 _dVLOAD _y201402060937 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA174-183
100	1		_aJohnson, F.E.A. _eautor _9316354
245	1	0	_aSyzygies and Homotopy Theory / _cby F.E.A. Johnson.
264		1	_aLondon : _bSpringer London, _c2012.
300			_axxiv, 294 páginas 1 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aAlgebra and Applications, _x1572-5553 ; _v17
500			_aSpringer eBooks
505	0		_aPreliminaries -- 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 = C¥ ´ F -- Conclusion .
520			_aThe 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 ´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.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9781447122937
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-1-4471-2294-4 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c287267 _d287267