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Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics pp 233–263Cite as

Introduction to Knot and Link Polynomials

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Part of the book series: NATO ASI Series ((ASIC,volume 235))

Abstract

The mathematical study of knots and links began around 1870. Now it is a chapter of topology having connections with several other domains including singularities of functions, dynamical systems, and the study of various enzymes acting on DNA molecules. Basic definitions are given, which are in particular intended to make existing knot tables intelligible, and various examples are described.

In 1928, J.W. Alexander first introduced a polynomial invariant for knots which now bears his name. In 1985, V.F.R. Jones defined another one variable polynomial. This has inspired a two variable link polynomial and, later, several other polynomial invariants. The notes offer an introduction to some of these recent ideas.

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Author information

Authors and Affiliations

  1. Section de Mathématiques, Université de Genève, C.P. 240, 1211, Genève 24, Switzerland

    P. de la Harpe

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  1. P. de la Harpe
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Editors and Affiliations

  1. Laboratory of Physical Chemistry, ETH-Zentrum, CH-8092, Zürich, Switzerland

    A. Amann

  2. Physical Chemistry Institute, University of Heidelberg, Im Neuenheimer Feld 253, D-6900, Heidelberg, Germany

    L. S. Cederbaum

  3. Institute of Physical Chemistry, Institut für Quantenchemie, Freie Universitat Berlin, Holbeinstrasse 48, D-1000, Berlin 45, Germany

    W. Gans

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© 1988 Kluwer Academic Publishers

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de la Harpe, P. (1988). Introduction to Knot and Link Polynomials. In: Amann, A., Cederbaum, L.S., Gans, W. (eds) Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics. NATO ASI Series, vol 235. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3005-6_17

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  • DOI: https://doi.org/10.1007/978-94-009-3005-6_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7850-4

  • Online ISBN: 978-94-009-3005-6

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