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Knot Invariants and Chern-Simons Theory

  • José M. F. Labastida
Conference paper
Part of the Progress in Mathematics book series (PM, volume 202)

Abstract

A brief review of the development of Chern-Simons gauge theory since its relation to knot theory was discovered in 1988 is presented. The presentation is done guided by a dictionary which relates knot theory concepts to quantum field theory ones. From the basic objects in both contexts the quantities leading to knot and link invariants are introduced and analysed. The quantum field theory approaches that have been developed to compute these quantities are reviewed. Perturbative approaches lead to Vassiliev or finite type invariants. Non-perturbative ones lead to polynomial or quantum group invariants. In addition, a brief discussion on open problems and future developments is included.

Keywords

Wilson Loop Double Point Feynman Rule Jones Polynomial Reidemeister Move 
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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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • José M. F. Labastida
    • 1
  1. 1.Departamento de Física de PartículasUniversidade de Santiago de CompostelaSantiago de CompostelaSpain

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