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

Abstract

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

6 pages, 1 figure

References in corpus (1)

• Corrigendum to "Knot Floer homology detects fibred knots"