Alternating numbers of torus knots with small braid index

Peter Feller; Simon Pohlmann; Raphael Zentner

doi:10.1512/iumj.2018.67.7302

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arXiv · 1508.05825

Alternating numbers of torus knots with small braid index

Peter Feller·Simon Pohlmann·Raphael Zentner

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Abstract

We calculate the alternating number of torus knots with braid index 4 and less. For the lower bound, we use the upsilon-invariant recently introduced by Ozsváth, Stipsicz, and Szabó. For the upper bound, we use a known bound for braid index $3$ and a new bound for braid index $4$. Both bounds coincide, so that we obtain a sharp result.

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BibTeX RIS

Peter Feller, Simon Pohlmann, Raphael Zentner. 2015-08-24. Alternating numbers of torus knots with small braid index. https://doi.org/10.1512/iumj.2018.67.7302

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