A note on changemaker lattices and Alexander polynomials of lens space knots

Jacob Caudell

A note on changemaker lattices and Alexander polynomials of lens space knots

Geometric Topology 2020-07-23 v1

Authors: Jacob Caudell

Abstract

We give an alternative proof of a recent theorem of Tange using the technology of changemaker lattices. Specifically, for $K\subset S^3$ a non-trivial knot with a lens space surgery, we give constraints on the Alexander polynomial of $K$ and the lens space surgery when the coefficient of $T^{g(K)-2}$ in $\Delta_K(T)$ is non-zero.

Keywords

changemaker lattice alexander polynomial lens space knot surgery knot

Cite

@article{arxiv.2007.11039,
  title  = {A note on changemaker lattices and Alexander polynomials of lens space knots},
  author = {Jacob Caudell},
  journal= {arXiv preprint arXiv:2007.11039},
  year   = {2020}
}

Comments

5 pages, 1 figure

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