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From Goeritz Matrices to Quasi-alternating Links

  • Józef H. PrzytyckiEmail author
Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (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.

Keywords

Jones Polynomial Regular Neighborhood Reidemeister Move Link Diagram Alexander Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Dept. of MathematicsThe George Washington UniversityWashingtonUSA
  2. 2.University of Texas at DallasDallasUSA

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