Cargando…
Syzygies and Homotopy Theory
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. S...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Springer London : Imprint: Springer,
2012.
|
| Edición: | 1st ed. 2012. |
| Colección: | Algebra and Applications,
17 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-1-4471-2294-4 | ||
| 003 | DE-He213 | ||
| 005 | 20220126101722.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 111116s2012 xxk| s |||| 0|eng d | ||
| 020 | |a 9781447122944 |9 978-1-4471-2294-4 | ||
| 024 | 7 | |a 10.1007/978-1-4471-2294-4 |2 doi | |
| 050 | 4 | |a QA174-183 | |
| 072 | 7 | |a PBG |2 bicssc | |
| 072 | 7 | |a MAT002010 |2 bisacsh | |
| 072 | 7 | |a PBG |2 thema | |
| 082 | 0 | 4 | |a 512.2 |2 23 |
| 100 | 1 | |a Johnson, F.E.A. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Syzygies and Homotopy Theory |h [electronic resource] / |c by F.E.A. Johnson. |
| 250 | |a 1st ed. 2012. | ||
| 264 | 1 | |a London : |b Springer London : |b Imprint: Springer, |c 2012. | |
| 300 | |a XXIV, 296 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Algebra and Applications, |x 2192-2950 ; |v 17 | |
| 505 | 0 | |a 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 = C¥ ´ F -- Conclusion . | |
| 520 | |a 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 ´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 | |a Group theory. | |
| 650 | 0 | |a Commutative algebra. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 1 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Commutative Rings and Algebras. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781447158127 |
| 776 | 0 | 8 | |i Printed edition: |z 9781447122937 |
| 776 | 0 | 8 | |i Printed edition: |z 9781447122951 |
| 830 | 0 | |a Algebra and Applications, |x 2192-2950 ; |v 17 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4471-2294-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||