Displaying similar documents to “On the Slice Genus of Knots.”

Knots of (canonical) genus two

A. Stoimenow (2008)

Fundamenta Mathematicae

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We give a description of all knot diagrams of canonical genus 2 and 3, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic volume for canonical (weak) genus 2 knots. We also study the values of the link polynomials at roots of unity, extending denseness results of Jones. Using...

Knots with property R + .

Clark, Bradd Evans (1983)

International Journal of Mathematics and Mathematical Sciences

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Nonfibered knots and representation shifts

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.

Torus knots that cannot be untied by twisting.

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.