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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2003
|
| Series: | London Mathematical Society lecture note series
301 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (ix, 267 pages) |
| ISBN: | 9780511550256 |
| DOI: | 10.1017/CBO9780511550256 |
Staff View
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| 100 | 1 | |a Johnson, F. E. A. |d 1946- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stable modules and the D(2)-problem |c F.E.A. Johnson |
| 246 | 1 | 3 | |a Stable Modules & the D(2)-Problem |
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| 490 | 0 | |a London Mathematical Society lecture note series |v 301 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a 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 | |
| 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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| 650 | 4 | |a Homotopy theory | |
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Record in the Search Index
| _version_ | 1804176883686834176 |
|---|---|
| any_adam_object | |
| author | Johnson, F. E. A. 1946- |
| author_facet | Johnson, F. E. A. 1946- |
| author_role | aut |
| author_sort | Johnson, F. E. A. 1946- |
| author_variant | f e a j fea feaj |
| building | Verbundindex |
| bvnumber | BV043941657 |
| classification_rvk | SK 260 SK 280 |
| collection | ZDB-20-CBO |
| 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511550256 (OCoLC)850267630 (DE-599)BVBBV043941657 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511550256 |
| format | Electronic eBook |
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| id | DE-604.BV043941657 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511550256 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350627 |
| oclc_num | 850267630 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (ix, 267 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Johnson, F. E. A. 1946- Verfasser aut Stable modules and the D(2)-problem F.E.A. Johnson Stable Modules & the D(2)-Problem Cambridge Cambridge University Press 2003 1 online resource (ix, 267 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 301 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Homotopy theory Group algebras Gruppenring (DE-588)4158469-7 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Niederdimensionale Topologie (DE-588)4280826-1 s Homotopietheorie (DE-588)4128142-1 s Gruppenring (DE-588)4158469-7 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-53749-0 https://doi.org/10.1017/CBO9780511550256 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Johnson, F. E. A. 1946- Stable modules and the D(2)-problem 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 Homotopy theory Group algebras Gruppenring (DE-588)4158469-7 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4158469-7 (DE-588)4280826-1 (DE-588)4128142-1 |
| title | Stable modules and the D(2)-problem |
| title_alt | Stable Modules & 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 Homotopy theory Group algebras Gruppenring (DE-588)4158469-7 gnd Niederdimensionale Topologie (DE-588)4280826-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Low-dimensional topology Homotopy theory Group algebras Gruppenring Niederdimensionale Topologie Homotopietheorie |
| url | https://doi.org/10.1017/CBO9780511550256 |
| work_keys_str_mv | AT johnsonfea stablemodulesandthed2problem AT johnsonfea stablemodulesthed2problem |