English

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