 
Summary: Samson Abramsky
TemperleyLieb Algebra:
From Knot Theory to
Logic and Computation
via Quantum Mechanics
1 Introduction
Our aim in this paper is to trace some of the surprising and beau
tiful connections which are beginning to emerge between a number of
apparently disparate topics.
1.1 Knot Theory
Vaughan Jones' discovery of his new polynomial invariant of knots in
1984 [26] triggered a spate of mathematical developments relating knot
theory, topological quantum field theory, and statistical physics inter
alia [44, 30]. A central r^ole, both in the initial work by Jones and in the
subsequent developments, was played by what has come to be known as
the TemperleyLieb algebra.1
1.2 Categorical Quantum Mechanics
Recently, motivated by the needs of Quantum Information and Com
putation, Abramsky and Coecke have recast the foundations of Quantum
Mechanics itself, in the more abstract language of category theory. The
