Affiliation:
1. Department of Mathematics, Osaka City University, Osaka 558-8585, Japan
Abstract
We give a lower bound for the alternation number of a knot by using the Rasmussen s-invariant and the signature of a knot. Then, we determine the torus knots with alternation number one and show that many torus knots are "far" from the alternating knots. As an application, we determine the almost alternating torus knots, solving a conjecture due to Adams et al.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
17 articles.
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1. The upsilon invariant at 1 of 3–braid
knots;Algebraic & Geometric Topology;2023-11-05
2. On alternating closed braids;Journal of Knot Theory and Its Ramifications;2021-03
3. Extremal Khovanov homology of Turaev genus one links;Fundamenta Mathematicae;2020
4. Invariants for Turaev genus one links;Communications in Analysis and Geometry;2018
5. The Turaev genus of torus knots;Journal of Knot Theory and Its Ramifications;2017-12