Graphs, surfaces and homology:
Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, M...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
|
| Ausgabe: | Third edition |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 251 pages) |
| ISBN: | 9780511779534 |
| DOI: | 10.1017/CBO9780511779534 |
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| 520 | |a Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study | ||
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Datensatz im Suchindex
| _version_ | 1804176887002431488 |
|---|---|
| any_adam_object | |
| author | Giblin, P. J. |
| author_facet | Giblin, P. J. |
| author_role | aut |
| author_sort | Giblin, P. J. |
| author_variant | p j g pj pjg |
| building | Verbundindex |
| bvnumber | BV043943274 |
| classification_rvk | SK 300 |
| collection | ZDB-20-CBO |
| contents | Introduction -- Graphs -- Closed surfaces -- Simplicial complexes -- Homology groups -- The question of invariance -- Some general theorems -- Two more general theorems -- Homology modulo 2 -- Graphs in surfaces --Appendix. Abelian groups |
| ctrlnum | (ZDB-20-CBO)CR9780511779534 (OCoLC)839014947 (DE-599)BVBBV043943274 |
| 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/CBO9780511779534 |
| edition | Third edition |
| format | Electronic eBook |
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| id | DE-604.BV043943274 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:19Z |
| institution | BVB |
| isbn | 9780511779534 |
| language | English |
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| oclc_num | 839014947 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xx, 251 pages) |
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| publishDate | 2010 |
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| publisher | Cambridge University Press |
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| spelling | Giblin, P. J. Verfasser aut Graphs, surfaces and homology Peter Giblin Graphs, Surfaces & Homology Third edition Cambridge Cambridge University Press 2010 1 online resource (xx, 251 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Graphs -- Closed surfaces -- Simplicial complexes -- Homology groups -- The question of invariance -- Some general theorems -- Two more general theorems -- Homology modulo 2 -- Graphs in surfaces --Appendix. Abelian groups Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study Algebraic topology Homologietheorie (DE-588)4141714-8 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 s 1\p DE-604 Homologietheorie (DE-588)4141714-8 s 2\p DE-604 Algebraische Topologie (DE-588)4120861-4 s 3\p DE-604 Erscheint auch als Druckausgabe 978-0-521-15405-5 Erscheint auch als Druckausgabe 978-0-521-76665-4 https://doi.org/10.1017/CBO9780511779534 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Giblin, P. J. Graphs, surfaces and homology Introduction -- Graphs -- Closed surfaces -- Simplicial complexes -- Homology groups -- The question of invariance -- Some general theorems -- Two more general theorems -- Homology modulo 2 -- Graphs in surfaces --Appendix. Abelian groups Algebraic topology Homologietheorie (DE-588)4141714-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4120861-4 (DE-588)4140988-7 |
| title | Graphs, surfaces and homology |
| title_alt | Graphs, Surfaces & Homology |
| title_auth | Graphs, surfaces and homology |
| title_exact_search | Graphs, surfaces and homology |
| title_full | Graphs, surfaces and homology Peter Giblin |
| title_fullStr | Graphs, surfaces and homology Peter Giblin |
| title_full_unstemmed | Graphs, surfaces and homology Peter Giblin |
| title_short | Graphs, surfaces and homology |
| title_sort | graphs surfaces and homology |
| topic | Algebraic topology Homologietheorie (DE-588)4141714-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Algebraic topology Homologietheorie Algebraische Topologie Abelsche Gruppe |
| url | https://doi.org/10.1017/CBO9780511779534 |
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