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Knots in mathematics and physics

Part of the Lecture Notes in Mathematics book series (LNM,volume 1525)

Abstract

Mathematical knot theory began in the nineteenth century as a result of questions about fluid flow and electromagnetism. In the twentieth century, it became a part of topology, the study of smooth deformations.

In recent years, knot theory has gone back to its physical origins in an interplay of mathematical analysis, topology, statistical mechanics and quantum field theory. It is far from clear what will emerge from these developments.

Keywords

  • Conformal Block
  • Braid Group
  • Conformal Field Theory
  • Alexander Polynomial
  • WZNW Model

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.

Fields Medal 1990 for the discovery of a 1-parameter representation of the classical braid groups into a family of C*-algebras, which led to a polynomial invariant of links. His work has greatly stimulated the recent development of research in C*-algebras, statistical mechanics, representations of quantum groups, knot theory and invariants of 3-dimensional manifolds.

Transcribed from the videotape of the talk by Carme Safont; revised and supplemented by the author.

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© 1992 Springer-Verlag

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Jones, V.F.R. (1992). Knots in mathematics and physics. In: Casacuberta, C., Castellet, M. (eds) Mathematical Research Today and Tomorrow. Lecture Notes in Mathematics, vol 1525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089206

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  • DOI: https://doi.org/10.1007/BFb0089206

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56011-1

  • Online ISBN: 978-3-540-47341-1

  • eBook Packages: Springer Book Archive