Guts of Surfaces and the Colored Jones Polynomial
This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of...
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2013. |
| Schriftenreihe: | Lecture Notes in Mathematics
2069 |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
L'impression du document génère 178 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Guts of surfaces and the colored Jones polynomial, David Futer, Efstratia Kalfagianni, Jessica Purcell, 2013, Heidelberg, Springer, 1 vol. (X-170 p.), Lecture notes in mathematics, 978-3-642-33301-9 • Guts of Surfaces and the Colored Jones Polynomial, Texte imprimé, 9783642333033 |
| Zusammenfassung: | This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials.Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants |
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| Beschreibung: | L'impression du document génère 178 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. Index |
| ISBN: | 9783642333026 |
| ISSN: | 1617-9692 |
| Zugangseinschränkungen: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |