In the mid-1980's, Abhay Ashtekar discovered a reformulation of
general relativity in terms of what are now called the "new
variables". This led to a rapid series of developments, and in 1990
Carlo Rovelli and Lee Smolin published a paper entitled "Loop
representation of quantum general relativity", in which, among
other things, it was shown that there is a space of solutions to
the constraint equations of quantum gravity consisting of link
invariants. The discovery of relations between quantum gravity and
the theory of knots and links came as quite a surprise, since the
topics had been regarded as quite remote from each other. This
volume is the proceedings of a workshop held in 1993 at the
University of California at Riverside. The purpose of the workshop
was to bring together researchers in knot theory and quantum
gravity and form more bridges between the two subjects. Most of the
talks were given by researchers whose work has significance for
both subjects. This volume contains expository papers as well as
new results, and should serve as a guide for mathematicians and
physicists seeking to understand this rapidly developing area of
research.
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