Knots, Links, and Physics

  • Michael Monastyrsky
Part of the Modern Birkhäuser Classics book series (MBC)


Knots are the oldest object of study in topology. They form the subject matter of the greater part of Listing’s first treatise, Vorstudien zur Topologie. This venerable division of topology, which flourished in the late 1920’s and early 1930’s, withered and faded away after the war. Such things happen to entire subjects as well as to people. It was not that there were no outstanding unsolved problems left in knot theory. For example, the following natural problem remained open: How can a knot be distinguished from its mirror image? The main goal of researchers was to find systems of knot invariants that would provide a simple procedure to distinguish knots. The most important knot invariant, which made it possible to distinguish knots quite simply in a number of cases, was a polynomial invariant, more precisely the Laurent invariant, discovered by the American mathematician J.W. Alexander (1888–1971). The Alexander polynomial Al(t) is symmetric under the change of variable\(t \mapsto \frac{1}{t}\) and does not make it possible to distinguish two knots that are mirror images of each other.


Braid Group Topological Invariant Jones Polynomial Alexander Polynomial Topological Field Theory 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Michael Monastyrsky
    • 1
  1. 1.Department of Theoretical PhysicsInsitute for Theoretical and Experimental PhysicsMoscowRussia

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