Jones polynomials, volume and essential knot surfaces: a survey

David Futer; Efstratia Kalfagianni; Jessica S. Purcell

Displaying similar documents to “Jones polynomials, volume and essential knot surfaces: a survey”

On the Mahler measure of Jones polynomials under twisting.

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Relations between the Jones and Q polynomials for 2-bridge and 3-braid links.

Tazio Kanenobu (1989)

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A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds

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...

Signature of rotors

Mieczysław K. Dąbkowski, Makiko Ishiwata, Józef H. Przytycki, Akira Yasuhara (2004)

Fundamenta Mathematicae

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Rotors were introduced as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we show that the Tristram-Levine signature is preserved by orientation-preserving rotations. Moreover, we show that any link invariant obtained from the characteristic polynomial of the Goeritz matrix, including the Murasugi-Trotter signature, is not changed by rotations. In 2001, P. Traczyk showed that the Conway polynomials of any pair of orientation-preserving rotants coincide....

Divisibility of twisted Alexander polynomials and fibered knots

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 $S L (2, 𝔽)$ -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree $4 g - 2$ for a fibered knot of genus $g$ .

On polynomials taking small values at integral arguments II

Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)

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On stability of Alexander polynomials of knots and links (survey)

Mikami Hirasawa, Kunio Murasugi (2014)

Banach Center Publications

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We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.

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Melvin, Paul, Shrestha, Sumana (2005)

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The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries

Hitoshi Murakami (2004)

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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.