The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kau¤man. Borisavljevíc, Došen and Petríc gave a complete proof of its abstract presentation by generators and relations, and suggested the name ‘Kau¤man monoid’. We bring the theory of semigroups to the study of a certain …nite homomorphic image o...

We give a new definition of the knot invariant associated to the Lie algebra suNC1 . Knowing these for all N is equivalent to knowing the HOMFLY polynomial. Our definition requires that the knot or link be presented as the plat closure of a braid. The invariant is then a homological intersection pairing between two immersed manifolds in a configuration space of points in a disk. This generalize...

We present a systematic study of the thermodynamics of two and three-dimensional generalized Lennard-Jones (LJ) systems focusing on the relationship between the range of the potential, the system density and its dimension. We found that the existence of negative specific heats depends on these three factors and not only on the potential range and the density of the system as stated in recent co...

The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coefficients of the Jones polynomial is bounded from above and from below by const...

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagra...