Behavior of knot invariants under genus 2 mutation.
Dunfield, Nathan M., Garoufalidis, Stavros, Shumakovitch, Alexander, Thistlethwaite, Morwen (2010)
The New York Journal of Mathematics [electronic only]
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Dunfield, Nathan M., Garoufalidis, Stavros, Shumakovitch, Alexander, Thistlethwaite, Morwen (2010)
The New York Journal of Mathematics [electronic only]
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Simon Blatt, Philipp Reiter (2014)
Molecular Based Mathematical Biology
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Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled”...
Gabriela Hinojosa, Alberto Verjovsky (2006)
Revista Matemática Complutense
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In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.
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...
Nafaa Chbili (2003)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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 .
Melvin, Paul, Shrestha, Sumana (2005)
Geometry & Topology
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Y. Diao, C. Ernst, A. Montemayor, E. Rawdon, U. Ziegler (2014)
Molecular Based Mathematical Biology
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It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant) bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular...
Garoufalidis, Stavros, Lan, Yueheng (2005)
Algebraic & Geometric Topology
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