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...
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| Auteur principal: | |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2012. |
| Collection: | Algebra and Applications
17 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Syzygies and homotopy theory, by F.E.A. Johnson, London, Springer, 2012, 1 vol. (XXIV-294 p., Algebra and applications, 978-1-447-12293-7 |
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| 009 | PPN157510158 | ||
| 020 | |a 9781447122944 |z 9781447122944 | ||
| 020 | |a 9781447122944 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.2 | ||
| 100 | 1 | |a Johnson, Francis Edward Anthony, |d 1946- | |
| 245 | 1 | 0 | |a Syzygies and homotopy theory |c by F. E. A. Johnson. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Algebra and Applications |v 17 |x 2192-2950 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 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 | |a Groupes, Théorie des | ||
| 650 | |a Anneaux commutatifs | ||
| 776 | 0 | |0 169851222 |t Syzygies and homotopy theory |f by F.E.A. Johnson |c London |n Springer |d 2012 |p 1 vol. (XXIV-294 p. |s Algebra and applications |z 978-1-447-12293-7 | |
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| 856 | 4 | |5 180339901:753966670 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-1-4471-2294-4 |z Accès INSA CVL | |
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