Abstract
According to a formula by Gordon and Litherland \cite{GordonLitherland}, the signature $\sigma (K)$ of a knot $K$ can be computed as $\sigma (K) = \sigma (G) - \mu$, where $G$ is the Goeritz matrix of a projection $D$ of $K$ and $\mu$ is a ``correction term,'' read off from the projection $D$. In this article, we consider the family of two bridge knots $K_{p/q}$ and compute the signature of the Goeritz matrices of their ``standard projections,'' $D_{p/q}$, by explicitly diagonalizing the Goertiz matrix over the rationals. We give applications to signature computations and concordance questions.
Citation
Michael Gallaspy. Stanislav Jabuka. "The Goeritz matrix and signature of a two bridge knot." Rocky Mountain J. Math. 45 (4) 1119 - 1145, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1119
Information