On the cusp shape of hyperbolic knots (Q2805390)

If \(K\) is a hyperbolic knot, then the holonomies of the meridian and longitude of \(K\) can be given by the pair of matrices NEWLINE\[NEWLINE \begin{pmatrix} 1 &1 \\ 0 & 1\end{pmatrix}, \begin{pmatrix} 1& c \\ 0 & 1\end{pmatrix}NEWLINE\]NEWLINE where \(c\) is a complex number called the cusp shape of \(K\). It is a topological invariant of \(K\). This paper provides a formula for the cusp shape of \(K\) in terms of the Hessian of the potential function associated to a knot diagram of \(K\).