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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Garoufalidis, Stavros, Lan, Yueheng (2005)
Algebraic & Geometric Topology
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Melvin, Paul, Shrestha, Sumana (2005)
Geometry & Topology
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Dunfield, Nathan M., Garoufalidis, Stavros (2004)
Algebraic & Geometric Topology
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Wei Tian, Xue Lei, Louis H. Kauffman, Jie Liang (2017)
Molecular Based Mathematical Biology
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Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class...
David Futer, Efstratia Kalfagianni, Jessica S. Purcell (2014)
Banach Center Publications
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This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.
Kalfagianni, Efstratia (2004)
Algebraic & Geometric Topology
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Hitoshi Murakami (2004)
Fundamenta Mathematicae
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I describe how the colored Jones polynomials of the figure-eight knot determine the volumes of the three-manifolds obtained by Dehn surgeries along it, according to my joint work with Y. Yokota.
Józef Przytycki (1995)
Banach Center Publications
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We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones, transplants into knot theory the idea of the Yang-Baxter equation with the spectral parameter (idea employed by Baxter in the theory of solvable models in statistical...
Paweł Traczyk (1995)
Banach Center Publications
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Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)
Algebraic & Geometric Topology
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Teruaki Kitano, Takayuki Morifuji (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree for a fibered knot of genus .
Ng, Lenhard L. (2001)
Algebraic & Geometric Topology
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