State invariants of two-bridge knots
Geometric Topology
2017-10-30 v2
Abstract
In this paper, we consider generalizations of the Alexander polynomial and signature of 2-bridge knots by considering the Gordon-Litherland bilinear forms associated to essential state surfaces of the 2-bridge knots. We show that the resulting invariants are well-defined and explore properties of these invariants. Finally we realize the boundary slopes of the essential surfaces as a difference of signatures of the knot.
Keywords
Cite
@article{arxiv.1708.00916,
title = {State invariants of two-bridge knots},
author = {Cynthia L. Curtis and Vincent Longo},
journal= {arXiv preprint arXiv:1708.00916},
year = {2017}
}
Comments
14 pages, 3 figures