Articles liés à Guts of Surfaces and the Colored Jones Polynomial
Synopsis
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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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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Guts of Surfaces and the Colored Jones Polynomial
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Springer Berlin Heidelberg, 2012
ISBN 10 : 364233301X
ISBN 13 : 9783642333019
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Guts of Surfaces and the Colored Jones Polynomial
Edité par
Springer Berlin Heidelberg, 2012
ISBN 10 : 364233301X
ISBN 13 : 9783642333019
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Kartoniert / Broschiert. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Relates all central areas of modern 3-dimensional topologyThe first monograph which initiates a systematic study of relations between quantum and geometric topologyAppeals to a broad audience of 3-dimensional topologists: combines tools fro. N° de réf. du vendeur 5057224
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Guts of Surfaces and the Colored Jones Polynomial (Lecture Notes in Mathematics, 2069)
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Guts of Surfaces and the Colored Jones Polynomial
Edité par
Springer Berlin Heidelberg, 2012
ISBN 10 : 364233301X
ISBN 13 : 9783642333019
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783642333019
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Guts of Surfaces and the Colored Jones Polynomial
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Springer Berlin Heidelberg Dez 2012, 2012
ISBN 10 : 364233301X
ISBN 13 : 9783642333019
Neuf
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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 184 pp. Englisch. N° de réf. du vendeur 9783642333019
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Guts of Surfaces and the Colored Jones Polynomial
Vendeur : Chiron Media, Wallingford, Royaume-Uni
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Guts of Surfaces and the Colored Jones Polynomial
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Brossura. Etat : fine. 2012; br., pp. 184, cm 23x13,5. Libro. N° de réf. du vendeur 1663769
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Guts of Surfaces and the Colored Jones Polynomial
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2012, 2012
ISBN 10 : 364233301X
ISBN 13 : 9783642333019
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 184 pp. Englisch. N° de réf. du vendeur 9783642333019
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Vendeur : Books Puddle, New York, NY, Etats-Unis
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