From Goeritz matrices to quasi-alternating links

Details From Goeritz matrices to quasi-alternating links From Goeritz matrices to quasi-alternating links

2009-09-06

arxiv.org/abs/0909.1118v1

Mathematics

Geometric Topology

76 pages, 75 figures

Scientific paper

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 as 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. Chapter IV of the book "KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots will be based on this survey,

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