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arXiv · 2007.14629

A characterization of $T_{2g+1,2}$ among alternating knots

Yi Ni
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Abstract

Let $K$ be a genus $g$ alternating knot with Alexander polynomial $Δ_K(T)=\sum_{i=-g}^ga_iT^i$. We show that if $|a_g|=|a_{g-1}|$, then $K$ is the torus knot $T_{2g+1,\pm2}$. This is a special case of the Fox Trapezoidal Conjecture. The proof uses Ozsváth and Szabó's work on alternating knots.

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Yi Ni. 2020-07-29. A characterization of $T_{2g+1,2}$ among alternating knots. https://arxiv.org/abs/2007.14629

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