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2015 The Goeritz matrix and signature of a two bridge knot
Michael Gallaspy, Stanislav Jabuka
Rocky Mountain J. Math. 45(4): 1119-1145 (2015). DOI: 10.1216/RMJ-2015-45-4-1119

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

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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

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 1333.57011
MathSciNet: MR3418186
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1119

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 4 • 2015
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