000 03664nam a22004695i 4500
001 978-1-4471-2294-4
003 DE-He213
005 20180115171509.0
007 cr nn 008mamaa
008 111116s2012 xxk| s |||| 0|eng d
020 _a9781447122944
_9978-1-4471-2294-4
024 7 _a10.1007/978-1-4471-2294-4
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.2
_223
100 1 _aJohnson, F.E.A.
_eauthor.
245 1 0 _aSyzygies and Homotopy Theory
_h[electronic resource] /
_cby F.E.A. Johnson.
264 1 _aLondon :
_bSpringer London,
_c2012.
300 _aXXIV, 296 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgebra and Applications,
_x1572-5553 ;
_v17
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.
650 0 _aMathematics.
650 0 _aCommutative algebra.
650 0 _aCommutative rings.
650 0 _aGroup theory.
650 1 4 _aMathematics.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aCommutative Rings and Algebras.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447122937
830 0 _aAlgebra and Applications,
_x1572-5553 ;
_v17
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-2294-4
912 _aZDB-2-SMA
999 _c370405
_d370405