**Connections between CFT and Topology via Knot Theory**

**R.J. Lawrence**

**Abstract: **
In this paper we shall discuss some of the isomorphisms
established between the approach to conformal field theory on
**P**^1 of Tsuchiya & Kanie
MR89m:81166,
and the topological construction of braid group representations of the
author's
thesis.
These approaches both lead, in the simplest cases, to the
one-variable Jones polynomial invariant of links, but can be generalised to
give other invariants. The case of higher spin representations of
*sl(2)* is discussed from the point of view of both approaches, and is
used to re-interpret the well known connection with cabled links. The
structure of the braid group representation obtained is also discussed in
both the spin-half and higher spin cases, and is extended to give a
representation of the category of tangles.

**Keywords: **knot theory, braid group, Jones polynomial, quantum
groups, Yang-Baxter equation, conformal field theory, monodromy
representation, Gauss-Manin connection, Knizhnik-Zamolodchikov equation

**AMS subject classification: ** 20F36 32G34 57M25 81T40

**Length: **10 pages

**Reference: *** Lecture Notes in Physics * **375** (1991)
245-254.
MR1134160 (93f:20051) (review by * Toshitake Kohno *.)

*Last updated on September 4th, 1996.*

ruthel@math.huji.ac.il