The work of Vaughan F. R. Jones. (English) Zbl 0743.01023

Birman, Joan S.

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 9-18 (1991).

[For the entire collection see Zbl 0741.00019.]
The Fields Medal was awarded to V. F. R. Jones at ICM’90. Why? This paper gives a concentrated answer and describes the beautiful results of Jones in a clearly way useful also for readers not specialized in geometric topology. The central result is Jones’ index theorem. The author refers to the connection of this theorem to knot and link theorem in \(R^ 3\). Some other theorems of Jones are formulated. His work is related to statistical mechanics. Contributions to quantum groups, Dynkin diagrams and representations of Lie algebras are pointed out. The author comments the history of some actual mathematical problems. This is an excellent paper to appreciate the mathematics of V. F. R. Jones!

Reviewer: W.H.Schmidt (Greifswald)

MSC:

01A65	Development of contemporary mathematics
54-03	History of general topology

Keywords:

Fields medal; index theorem; Dynkin diagram; quantum group; knot; link; geometric topology; statistical mechanics

Citations:

Zbl 0741.00019