Japanese Journal of Mathematics

, Volume 11, Issue 1, pp 69–111

Knots, groups, subfactors and physics

Takagi Lectures

DOI: 10.1007/s11537-016-1529-x

Cite this article as:
Jones, V.F.R. Jpn. J. Math. (2016) 11: 69. doi:10.1007/s11537-016-1529-x


Groups have played a big role in knot theory. We show how subfactors (subalgebras of certain von Neumann algebras) lead to unitary representations of the braid groups and Thompson’s groups \({F}\) and \({T}\). All knots and links may be obtained from geometric constructions from these groups. And invariants of knots may be obtained as coefficients of these representations. We include an extended introduction to von Neumann algebras and subfactors.

Keywords and phrases

subfactors planar algebras 

Mathematics Subject Classification (2010)

46L37 (46L54) 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2016

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA
  2. 2.Department of MathematicsKyoto UniversityKyotoJapan