Representation of -knots.
Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Similarity:
Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Similarity:
Daniel S. Silver, Susan G. Williams (2009)
Banach Center Publications
Similarity:
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.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
Similarity:
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
Similarity:
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
Similarity:
Maciej Borodzik, Krzysztof Oleszkiewicz (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We study properties of the signature function of the torus knot . First we provide a very elementary proof of the formula for the integral of the signature over the circle. We also obtain a closed formula for the Tristram-Levine signature of a torus knot in terms of Dedekind sums.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
Similarity:
P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
Similarity:
We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Ying-Qing Wu (1993)
Mathematische Annalen
Similarity:
Greg Friedman (2007)
Fundamenta Mathematicae
Similarity:
We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.
Yasutaka Nakanishi (1996)
Revista Matemática de la Universidad Complutense de Madrid
Similarity:
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.
Skip Pennock (2005)
Visual Mathematics
Similarity:
Prabhakar Madeti, Rama Mishra (2006)
Fundamenta Mathematicae
Similarity:
We discuss polynomial representations for 2-bridge knots and determine the minimal degree sequence for all such knots. We apply the connection between rational tangles and 2-bridge knots.
Dennis Roseman (1975)
Fundamenta Mathematicae
Similarity:
Perko, Kenneth A. jr. (1979)
Portugaliae mathematica
Similarity:
Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
Similarity:
We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.