Graphs on surfaces : dualities, polynomials, and knots
Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdepend...
Gardado en:
| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
New York, NY :
Springer New York
2013.
Cham : Springer Nature |
| Series: | SpringerBriefs in Mathematics
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| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 149 p. Date de publication et éditeur d après le site du fournisseur Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Graphs on surfaces, dualities, polynomials, and knots, Joanna A. Ellis-Monaghan, Iain Moffatt, 2013, New York, Springer, 1 vol. (XI-139 p.), SpringerBriefs in mathematics, 978-1-461-46970-4 |
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| 041 | 0 | |a eng | |
| 082 | |a 511.5 | ||
| 100 | 1 | |a Ellis-Monaghan, Joanna A., |d 19..- | |
| 245 | 1 | 0 | |a Graphs on surfaces : |b dualities, polynomials, and knots |c by Joanna A. Ellis-Monaghan, Iain Moffatt. |
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c 2013. | ||
| 490 | 0 | |a SpringerBriefs in Mathematics |x 2191-8198 | |
| 500 | |a L'impression du document génère 149 p. | ||
| 500 | |a Date de publication et éditeur d après le site du fournisseur | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliographie p. 131-134. Index | ||
| 505 | 1 | |a 1. Embedded Graphs 2. Generalised Dualities 3. Twisted duality, cycle family graphs, and embedded graph equivalence 4. Interactions with Graph Polynomials 5. Applications to Knot Theory .- References Index | |
| 505 | 0 | |a 1, Embedded Graphs -- 2 Generalised Dualities -- 3 Twisted Duality, Cycle Family Graphs, and Embedded Graph Equivalence -- 4, Interactions with Graph Polynomials -- 5, Applications to Knot Theory -- 1.1, Embedded Graphs and Their Representations -- 1.2, Further Properties of Embedded Graphs -- 1.3, Petrials ofEmbeddedGraphs -- 1.4, Geometric Duality -- 1.5, Medial Graphs, Tait Graphs, and Duality -- 2.1, Partial Petrials -- 2.2, Partial Duals -- 2.3, Twisted Duality -- 2.4, The Ribbon Group and its Action -- 3.1, Characterising Orb(G) -- 3.2, A Structural Hierarchy and Corresponding Dualities -- 3.3, Properties of SomeSpecial Orbits -- 4.1, Classical Graph Polynomials -- 4.2, Deletion, Contraction, and Medial Graphs -- 4.3, Twisted Duals and the Topological Transition Polynomial -- 4.4, The Penrose Polynomial -- 4.5, Topological Tutte Polynomials -- 4.6, Relating the Penrose and Topochromatic Polynomials -- 5.1, Knots and Links -- 5.2, Virtual Links -- 5.3, Presenting Links as Embedded Graphs -- 5.4, The Jones Polynomial and Graph Polynomials -- 5.5, The HOMFLY-PT Polynomial and Graph Polynomials | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise | ||
| 650 | |a Topologie | ||
| 650 | |a Topologie algébrique | ||
| 650 | |a Théorie des graphes | ||
| 700 | 1 | |a Moffatt, Iain, |d 19..- |4 aut | |
| 776 | 0 | |0 175085986 |t Graphs on surfaces |o dualities, polynomials, and knots |f Joanna A. Ellis-Monaghan, Iain Moffatt |d 2013 |c New York |n Springer |p 1 vol. (XI-139 p.) |s SpringerBriefs in mathematics |z 978-1-461-46970-4 | |
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| 997 | |0 946476 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||