Metacyclic groups and the D(2) problem:
"The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved. The problem is parametrized by the...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2021
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved. The problem is parametrized by the fundamental group of the spaces involved; that is, each group G has its own D(2) problem whose difficulty varies considerably with the individual nature of G. This book solves the D(2) problem for a large, possibly infinite, number of finite metacyclic groups G(p, q). Prior to this the author had solved the D(2) problem for the groups G(p, 2). However, for q > 2, the only previously known solutions were for the groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct calculation by two of the author's students, Jonathan Remez (2011) and Jason Vittis (2019). The method employed is heavily algebraic and involves precise analysis of the integral representation theory of G(p, q). Some noteworthy features are a new cancellation theory of modules (Chapters 10 and 11) and a simplified treatment (Chapters 5 and 12) of the author's theory of Swan homomorphisms"--Publisher's website |
| Beschreibung: | 1 online resource (xiii, 357 p.) |
| ISBN: | 9789811222764 |
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| 520 | |a "The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved. The problem is parametrized by the fundamental group of the spaces involved; that is, each group G has its own D(2) problem whose difficulty varies considerably with the individual nature of G. This book solves the D(2) problem for a large, possibly infinite, number of finite metacyclic groups G(p, q). Prior to this the author had solved the D(2) problem for the groups G(p, 2). However, for q > 2, the only previously known solutions were for the groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct calculation by two of the author's students, Jonathan Remez (2011) and Jason Vittis (2019). The method employed is heavily algebraic and involves precise analysis of the integral representation theory of G(p, q). Some noteworthy features are a new cancellation theory of modules (Chapters 10 and 11) and a simplified treatment (Chapters 5 and 12) of the author's theory of Swan homomorphisms"--Publisher's website | ||
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Datensatz im Suchindex
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| author | Johnson, F. E. A. 1946- |
| author_facet | Johnson, F. E. A. 1946- |
| author_role | aut |
| author_sort | Johnson, F. E. A. 1946- |
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| 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 | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV047192189 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:48:17Z |
| indexdate | 2024-07-10T09:05:13Z |
| institution | BVB |
| isbn | 9789811222764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032597361 |
| oclc_num | 1241668613 |
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| physical | 1 online resource (xiii, 357 p.) |
| psigel | ZDB-124-WOP |
| publishDate | 2021 |
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| publishDateSort | 2021 |
| publisher | World Scientific |
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| spelling | Johnson, F. E. A. 1946- Verfasser aut Metacyclic groups and the D(2) problem by Francis E A Johnson Singapore World Scientific 2021 1 online resource (xiii, 357 p.) txt rdacontent c rdamedia cr rdacarrier "The D(2) problem is a fundamental problem in low dimensional topology. In broad terms, it asks when a three-dimensional space can be continuously deformed into a two-dimensional space without changing the essential algebraic properties of the spaces involved. The problem is parametrized by the fundamental group of the spaces involved; that is, each group G has its own D(2) problem whose difficulty varies considerably with the individual nature of G. This book solves the D(2) problem for a large, possibly infinite, number of finite metacyclic groups G(p, q). Prior to this the author had solved the D(2) problem for the groups G(p, 2). However, for q > 2, the only previously known solutions were for the groups G(7, 3), G(5, 4) and G(7, 6), all done by difficult direct calculation by two of the author's students, Jonathan Remez (2011) and Jason Vittis (2019). The method employed is heavily algebraic and involves precise analysis of the integral representation theory of G(p, q). Some noteworthy features are a new cancellation theory of modules (Chapters 10 and 11) and a simplified treatment (Chapters 5 and 12) of the author's theory of Swan homomorphisms"--Publisher's website Low-dimensional topology Homotopy theory Group algebras Electronic books Erscheint auch als Druck-Ausgabe 9789811222757 https://www.worldscientific.com/worldscibooks/10.1142/11897#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Johnson, F. E. A. 1946- Metacyclic groups and the D(2) problem Low-dimensional topology Homotopy theory Group algebras |
| title | Metacyclic groups and the D(2) problem |
| title_auth | Metacyclic groups and the D(2) problem |
| title_exact_search | Metacyclic groups and the D(2) problem |
| title_exact_search_txtP | Metacyclic groups and the D(2) problem |
| title_full | Metacyclic groups and the D(2) problem by Francis E A Johnson |
| title_fullStr | Metacyclic groups and the D(2) problem by Francis E A Johnson |
| title_full_unstemmed | Metacyclic groups and the D(2) problem by Francis E A Johnson |
| title_short | Metacyclic groups and the D(2) problem |
| title_sort | metacyclic groups and the d 2 problem |
| topic | Low-dimensional topology Homotopy theory Group algebras |
| topic_facet | Low-dimensional topology Homotopy theory Group algebras |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11897#t=toc |
| work_keys_str_mv | AT johnsonfea metacyclicgroupsandthed2problem |