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State invariants of 2-bridge knots

Cynthia L. Curtis

http://orcid.org/0000-0001-8804-2827

Department of Mathematics & Statistics, The College of New Jersey, Ewing, NJ 08628, USA

E-mail Address: ccurtis@tcnj.edu

Corresponding author.

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and

Vincent Longo

Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA

E-mail Address: vlongo2@unl.edu

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https://doi.org/10.1142/S0218216518500165Cited by:0 (Source: Crossref)

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 with 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 essential surfaces as differences of signatures of the knot.

Keywords:

AMSC: 57M25, 57M27

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