Volume conjecture and asymptotic expansion of -series.

Hikami, Kazuhiro

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Displaying similar documents to “Volume conjecture and asymptotic expansion of $q$ -series.”

Kashaev's conjecture and the Chern-Simons invariants of knots and links.

Murakami, Hitoshi, Kurakami, Jun, Okamoto, Miyuki, Takata, Toshie, Yokota, Yoshiyuki (2002)

Experimental Mathematics

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Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2-bridge knot.

Garoufalidis, Stavros, Lan, Yueheng (2005)

Algebraic & Geometric Topology

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On the first two Vassiliev invariants.

Willerton, Simon (2002)

Experimental Mathematics

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Unknotting number and knot diagram.

Yasutaka Nakanishi (1996)

Revista Matemática de la Universidad Complutense de Madrid

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This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.

An operator invariant for handlebody-knots

Kai Ishihara, Atsushi Ishii (2012)

Fundamenta Mathematicae

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A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.

A glimpse at knot theory

Paweł Traczyk (1995)

Banach Center Publications

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Nonfibered knots and representation shifts

Daniel S. Silver, Susan G. Williams (2009)

Banach Center Publications

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A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.

All integral slopes can be Seifert fibered slopes for hyperbolic knots.

Motegi, Kimihiko, Song, Hyun-Jong (2005)

Algebraic & Geometric Topology

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On the AJ conjecture for cables of twist knots

Anh T. Tran (2015)

Fundamenta Mathematicae

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We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.

Positive knots, closed braids and the Jones polynomial

Alexander Stoimenow (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Using the recent Gauß diagram formulas for Vassiliev invariants of Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality, we prove several inequalities for positive knots relating their Vassiliev invariants, genus and degrees of the Jones polynomial. As a consequence, we prove that for any of the polynomials of Alexander/Conway, Jones, HOMFLY, Brandt-Lickorish-Millett-Ho and Kauffman there are only finitely many positive knots with the same polynomial and no...

Alexander polynomial, finite type invariants and volume of hyperbolic knots.

Kalfagianni, Efstratia (2004)

Algebraic & Geometric Topology

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Minimizing the presentation of a knot group.

Dugopolski, Mark J. (1985)

International Journal of Mathematics and Mathematical Sciences

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A partial order in the knot table.

Kitano, Teruaki, Suzuki, Masaaki (2005)

Experimental Mathematics

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Virtual knot invariants arising from parities

Denis Petrovich Ilyutko, Vassily Olegovich Manturov, Igor Mikhailovich Nikonov (2014)

Banach Center Publications

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In [12, 15] it was shown that in some knot theories the crucial role is played by parity, i.e. a function on crossings valued in {0,1} and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and to prove minimality theorems for knots. In the present paper, we generalise the notion of parity and construct parities with coefficients from an abelian group rather than ℤ₂ and investigate...

Displaying similar documents to “Volume conjecture and asymptotic expansion of q -series.”

Displaying similar documents to “Volume conjecture and asymptotic expansion of $q$ -series.”