Stable modules and the D(2)-problem /:
This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2003.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
301. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field. |
| Beschreibung: | 1 online resource (ix, 267 pages) |
| Bibliographie: | Includes bibliographical references (pages 262-265) and index. |
| ISBN: | 9781107362284 1107362288 |
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| 588 | 0 | |a Print version record. | |
| 520 | |a This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field. | ||
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| contents | 1. Orders in semisimple algebras -- 2. Representation of finite groups -- 3. Stable modules and cancellation theorems -- 4. Relative homological algebra -- 5. The derived category of a finite group -- 6. k-invariants -- 7. Groups of periodic cohomology -- 8. Algebraic homotopy theory -- 9. Stability theorems -- 10. The D(2)-problem -- 11. Poincare -- 3 complexes. |
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| indexdate | 2024-10-25T16:21:21Z |
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| spelling | Johnson, F. E. A. (Francis Edward Anthony), 1946- https://id.oclc.org/worldcat/entity/E39PCjC73QhvK7KT44k49DMxwy http://id.loc.gov/authorities/names/n2003007164 Stable modules and the D(2)-problem / F.E.A. Johnson. Cambridge, UK ; New York : Cambridge University Press, 2003. 1 online resource (ix, 267 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 301 Includes bibliographical references (pages 262-265) and index. 1. Orders in semisimple algebras -- 2. Representation of finite groups -- 3. Stable modules and cancellation theorems -- 4. Relative homological algebra -- 5. The derived category of a finite group -- 6. k-invariants -- 7. Groups of periodic cohomology -- 8. Algebraic homotopy theory -- 9. Stability theorems -- 10. The D(2)-problem -- 11. Poincare -- 3 complexes. Print version record. This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field. Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group algebras. http://id.loc.gov/authorities/subjects/sh85057472 Topologie de basse dimension. Homotopie. Algèbres de groupes. MATHEMATICS Topology. bisacsh Group algebras fast Homotopy theory fast Low-dimensional topology fast Gruppenring gnd http://d-nb.info/gnd/4158469-7 Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Niederdimensionale Topologie gnd http://d-nb.info/gnd/4280826-1 Grupos finitos. larpcal Álgebra. larpcal has work: Stable modules and the D(2)-problem (Text) https://id.oclc.org/worldcat/entity/E39PCFFJTyCV9Gcx9RvXGjYbgq https://id.oclc.org/worldcat/ontology/hasWork Print version: Johnson, F.E.A. (Francis Edward Anthony), 1946- Stable modules and the D(2)-problem. Cambridge, UK ; New York : Cambridge University Press, 2003 0521537495 (DLC) 2003046133 (OCoLC)51886466 London Mathematical Society lecture note series ; 301. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552341 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552341 Volltext |
| spellingShingle | Johnson, F. E. A. (Francis Edward Anthony), 1946- Stable modules and the D(2)-problem / London Mathematical Society lecture note series ; 1. Orders in semisimple algebras -- 2. Representation of finite groups -- 3. Stable modules and cancellation theorems -- 4. Relative homological algebra -- 5. The derived category of a finite group -- 6. k-invariants -- 7. Groups of periodic cohomology -- 8. Algebraic homotopy theory -- 9. Stability theorems -- 10. The D(2)-problem -- 11. Poincare -- 3 complexes. Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group algebras. http://id.loc.gov/authorities/subjects/sh85057472 Topologie de basse dimension. Homotopie. Algèbres de groupes. MATHEMATICS Topology. bisacsh Group algebras fast Homotopy theory fast Low-dimensional topology fast Gruppenring gnd http://d-nb.info/gnd/4158469-7 Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Niederdimensionale Topologie gnd http://d-nb.info/gnd/4280826-1 Grupos finitos. larpcal Álgebra. larpcal |
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| title | Stable modules and the D(2)-problem / |
| title_auth | Stable modules and the D(2)-problem / |
| title_exact_search | Stable modules and the D(2)-problem / |
| title_full | Stable modules and the D(2)-problem / F.E.A. Johnson. |
| title_fullStr | Stable modules and the D(2)-problem / F.E.A. Johnson. |
| title_full_unstemmed | Stable modules and the D(2)-problem / F.E.A. Johnson. |
| title_short | Stable modules and the D(2)-problem / |
| title_sort | stable modules and the d 2 problem |
| topic | Low-dimensional topology. http://id.loc.gov/authorities/subjects/sh85078631 Homotopy theory. http://id.loc.gov/authorities/subjects/sh85061803 Group algebras. http://id.loc.gov/authorities/subjects/sh85057472 Topologie de basse dimension. Homotopie. Algèbres de groupes. MATHEMATICS Topology. bisacsh Group algebras fast Homotopy theory fast Low-dimensional topology fast Gruppenring gnd http://d-nb.info/gnd/4158469-7 Homotopietheorie gnd http://d-nb.info/gnd/4128142-1 Niederdimensionale Topologie gnd http://d-nb.info/gnd/4280826-1 Grupos finitos. larpcal Álgebra. larpcal |
| topic_facet | Low-dimensional topology. Homotopy theory. Group algebras. Topologie de basse dimension. Homotopie. Algèbres de groupes. MATHEMATICS Topology. Group algebras Homotopy theory Low-dimensional topology Gruppenring Homotopietheorie Niederdimensionale Topologie Grupos finitos. Álgebra. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552341 |
| work_keys_str_mv | AT johnsonfea stablemodulesandthed2problem |