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Guts of Surfaces and the Colored Jones Polynomial
TLDR
We introduce new invariants for links in 3–manifolds, as well as invariants of hyperbolic knots. Expand
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THE HOMFLY POLYNOMIAL FOR LINKS IN RATIONAL HOMOLOGY 3-SPHERES
Abstract We use intrinsic 3-manifold topology to construct formal power series invariants for links in a large class of rational homology 3-spheres, which generalizes the 2-variable Jones polynomialExpand
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Turaev-Viro invariants, colored Jones polynomials and volume
We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples for which theExpand
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Finite type invariants for knots in 3-manifolds
Abstract We use the Jaco-Shalen and Johannson theory of the characteristic submanifold and the Torus theorem (Gabai, Casson-Jungreis) to develop an intrinsic finite type theory for knots inExpand
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The Jones polynomial and graphs on surfaces
TLDR
In this paper we show that the Jones polynomial of any link can be obtained from the Bollobas-Riordan-Tutte poynomial of a certain oriented ribbon graph associated to a link projection. Expand
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Cusp Areas of Farey Manifolds and Applications to Knot Theory
This paper gives the first explicit, two-sided estimates on the cusp area of once-punctured-torus bundles, 4-punctured sphere bundles, and two-bridge link complements. The input for these estimatesExpand
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Knot Cabling and the Degree of the Colored Jones Polynomial II
We continue our study of the degree of the colored Jones polynomial under knot cabling started in "Knot Cabling and the Degree of the Colored Jones Polynomial" (arXiv:1501.01574). Under certainExpand
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Quasifuchsian state surfaces
This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolicExpand
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FINITE TYPE INVARIANTS FOR KNOTS
We use the Jaco-Shalen and Johannson theory of the characteristic submanifold and the Torus theorem (Gabai, Casson-Jungreis) to develop an intrinsic finite tvne theory for knots in irreducibleExpand
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On knot adjacency
Abstract A knot K is called n -adjacent to the unknot if it admits a projection that contains n disjoint single crossings such that changing any 0 of these crossings, yields a projection of theExpand
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