State invariants of two-bridge knots

Cynthia L. Curtis; Vincent Longo

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arXiv · 1708.00916

State invariants of two-bridge knots

Cynthia L. Curtis·Vincent Longo

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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.

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Cynthia L. Curtis, Vincent Longo. 2017-08-02. State invariants of two-bridge knots. https://arxiv.org/abs/1708.00916

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