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From Goeritz Matrices to Quasi-alternating Links

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The Mathematics of Knots

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 1))

Abstract

Knot Theory is currently a very broad field. Even a long survey can only cover a narrow area. Here we concentrate on the path from Goeritz matrices to quasi-alternating links. On the way, we often stray from the main road and tell related stories, especially if they allow us to place the main topic in a historical context. For example, we mention that the Goeritz matrix was preceded by the Kirchhoff matrix of an electrical network. The network complexity extracted from the matrix corresponds to the determinant of a link. We assume basic knowledge of knot theory and graph theory, however, we offer a short introduction under the guise of a historical perspective.

The author was partially supported by the NSA grant (# H98230-08-1-0033), by the Polish Scientific Grant: Nr. N N201387034, by the GWU REF grant, and by the CCAS/UFF award.

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  1. Dept. of Mathematics, The George Washington University, Washington, DC, 20052, USA

    Józef H. Przytycki

  2. University of Texas at Dallas, Dallas, TX, USA

    Józef H. Przytycki

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  1. Department of Mathematics, University of Heidelberg, Im Neuenheimer Feld 288, Heidelberg, 69120, Germany

    Markus Banagl

  2. Department of Mathematics, University of Heidelberg, Im Neuenheimer Feld 288, Heidelberg, 69120, Germany

    Denis Vogel

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Przytycki, J.H. (2011). From Goeritz Matrices to Quasi-alternating Links. In: Banagl, M., Vogel, D. (eds) The Mathematics of Knots. Contributions in Mathematical and Computational Sciences, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15637-3_9

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