Abstract. We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative canonical quantum general relativity (loop quantum gravity). This leads naturally to a discussion of the Kodama wavefunction, a state which is conjectured to be the ground state of the gravitational field with positive cosmological constant. This review can serve as a self-contained introduction to loop quantum gravity and related areas. Our intent is to make the paper accessible to a wider audience that may include topologists, knot theorists, and other persons innocent of the physical background to this approach to quantum gravity.

PACS numbers: 04.20.Fy, 04.60.Ds, 04.60.Pp

Print publication: Issue 4 (21 February 2006)
Received 6 May 2005, in final form 30 November 2005
Published 31 January 2006