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...
שמור ב:
| Auteurs principaux: | , |
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| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
New York, NY :
Springer New York
2013.
Cham : Springer Nature |
| סדרה: | SpringerBriefs in Mathematics
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| נושאים: | |
| גישה מקוונת: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| הערה: |
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 |
תוכן הענינים:
- 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
- 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