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

Yi Ni

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

Geometric Topology 2020-07-30 v1

Authors: Yi Ni

Abstract

Let $K$ be a genus $g$ alternating knot with Alexander polynomial $\Delta_K(T)=\sum_{i=-g}^ga_iT^i$ . 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 Ozsv\'ath and Szab\'o's work on alternating knots.

Keywords

alternating knots torus knots alexander polynomial fox trapezoidal conjecture knot genus

Cite

@article{arxiv.2007.14629,
  title  = {A characterization of $T_{2g+1,2}$ among alternating knots},
  author = {Yi Ni},
  journal= {arXiv preprint arXiv:2007.14629},
  year   = {2020}
}

Comments

6 pages, 1 figure

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