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, to...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©2010.
|
| Ausgabe: | 3rd ed. |
| Schlagworte: | |
| Online-Zugang: | 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: | 1 online resource (xx, 251 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 239-242) and index. |
| ISBN: | 9780511902192 0511902190 9780511799044 0511799047 9780511779534 0511779534 |
Internformat
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| author_facet | Giblin, P. J. |
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| 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. |
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| discipline | Mathematik |
| edition | 3rd ed. |
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| spelling | Giblin, P. J. Graphs, surfaces and homology / Peter Giblin. 3rd ed. Cambridge ; New York : Cambridge University Press, ©2010. 1 online resource (xx, 251 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier "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"-- Provided by publisher. Includes bibliographical references (pages 239-242) and index. 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. Print version record. Algebraic topology. http://id.loc.gov/authorities/subjects/sh85003438 Topologie algébrique. MATHEMATICS Topology. bisacsh Algebraic topology fast Abelsche Gruppe gnd http://d-nb.info/gnd/4140988-7 Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 Homologietheorie gnd http://d-nb.info/gnd/4141714-8 Electronic books. has work: Graphs, surfaces and homology (Text) https://id.oclc.org/worldcat/entity/E39PCGh8w48Fqgj4DTfCtvDj83 https://id.oclc.org/worldcat/ontology/hasWork Print version: Giblin, P.J. Graphs, surfaces and homology. 3rd ed. Cambridge ; New York : Cambridge University Press, ©2010 9780521766654 (DLC) 2010022763 (OCoLC)642624649 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=331316 Volltext |
| 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. http://id.loc.gov/authorities/subjects/sh85003438 Topologie algébrique. MATHEMATICS Topology. bisacsh Algebraic topology fast Abelsche Gruppe gnd http://d-nb.info/gnd/4140988-7 Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 Homologietheorie gnd http://d-nb.info/gnd/4141714-8 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003438 http://d-nb.info/gnd/4140988-7 http://d-nb.info/gnd/4120861-4 http://d-nb.info/gnd/4141714-8 |
| title | Graphs, surfaces and 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. http://id.loc.gov/authorities/subjects/sh85003438 Topologie algébrique. MATHEMATICS Topology. bisacsh Algebraic topology fast Abelsche Gruppe gnd http://d-nb.info/gnd/4140988-7 Algebraische Topologie gnd http://d-nb.info/gnd/4120861-4 Homologietheorie gnd http://d-nb.info/gnd/4141714-8 |
| topic_facet | Algebraic topology. Topologie algébrique. MATHEMATICS Topology. Algebraic topology Abelsche Gruppe Algebraische Topologie Homologietheorie Electronic books. |
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