Mp-small summands increase knot width.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Skip Pennock (2005)
Visual Mathematics
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Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
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S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Perko, Kenneth A. jr. (1979)
Portugaliae mathematica
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Ying-Qing Wu (1993)
Mathematische Annalen
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P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
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We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Dennis Roseman (1975)
Fundamenta Mathematicae
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Mohamed Ait Nouh, Akira Yasuhara (2001)
Revista Matemática Complutense
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We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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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.