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State invariants of 2-bridge knots
Preview AbstractIn 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.