Braid group, knot theory and statistical mechanics
نویسندگان
چکیده
منابع مشابه
Braid Ordering and Knot Genus
The genus of knots is a one of the fundamental invariant and can be seen as a complexity of knots. In this note, we give a lower bound of genus using Dehornoy floor, which is a measure of complexity of braids in terms of braid ordering.
متن کاملStatistical Mechanics and Information Theory
Definition 1 (Spin Excess) For a system with N particles with spins ±m, the spin excess is given by how many particles more than N/2 have spin +m, i.e. S = N↑ − N2 where N↑ is the number of particles with spin +m. From Definition 1 and Equation (1) it follows that the total magnetic moment is given by M = 2mS. Theoretically, one could calculate the system’s magnetic moment at some point in time...
متن کاملQuantum Mechanics and Group Theory
where xi is the the Cartesian coordinate of a point particle of mass m, Fi is the external force applied to the particle, and the force is assumed to be conservative, the negative gradient of a potential energy function V (x). Newtonian mechanics for rigid bodies can be formulated in a similar way, and this approach can even be extended to relativistic point mechanics. The calculus of variation...
متن کاملKnot and Braid Invariants from Contact Homology
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology of certain Legendrian tori in fivedimensional contact manifolds. We present several computations and derive a relation between the knot invarian...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1990
ISSN: 0001-8708
DOI: 10.1016/0001-8708(90)90091-z