Unsigned State Models for the Jones Polynomial
نویسندگان
چکیده
منابع مشابه
Unsigned State Models for the Jones Polynomial
It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we sh...
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IN THIS PAPER I construct a state model for the (original) Jones polynomial [5]. (In [6] a state model was constructed for the Conway polynomial.) As we shall see, this model for the Jones polynomial arises as a normalization of a regular isotopy invariant of unoriented knots and links, called here the bracket polynomial, and denoted 〈K〉 for a link projectionK . The concept of regular isotopy w...
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Introduction: In recent years a number of fundamental ideas and methods of mathematical physics have penetrated through psychological barriers between physics and topology. In the knot theory this development was initiated by V. Jones who used von Neumann algebras to construct a new polynomial invariant of knots and links in the 3-dimensional sphere S 3. The Jones's discovery gave impetus to an...
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The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte-Carlo algorithms that can estimate general permanents. Given a planar diagram of a link L with n crossings, we define a 7n× 7n matrix whose permanent equals to the Jones polynomial of L. This result accompanied with recent ...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2011
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-011-0087-4