Coefficients and non-triviality of the Jones polynomial
نویسندگان
چکیده
منابع مشابه
Flag algebras and the stable coefficients of the Jones polynomial
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose elements give invariants of alternating links which strictly refine the first fo...
متن کاملNon-triviality of the A-polynomial for Knots in S3
The A-polynomial of a knot in S3 is a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL2C. Here, we show that a non-trivial knot in S3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU2-representations of Dehn surgeries on knots in S3. As a corollary, we show that if a conj...
متن کاملNon-triviality of the A-polynomial for knots in S
The A-polynomial of a knot in S defines a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL2C . Here, we show that a non-trivial knot in S 3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU2 -representations of Dehn surgeries on knots in S . As a corollary, we show that if...
متن کاملThe Jones Polynomial
A link is a finite family of disjoint, smooth, oriented or unoriented, closed curves in R or equivalently S. A knot is a link with one component. The Jones polynomial VL(t) is a Laurent polynomial in the variable √ t which is defined for every oriented link L but depends on that link only up to orientation preserving diffeomorphism, or equivalently isotopy, of R. Links can be represented by dia...
متن کاملZeroes of the Jones polynomial
We study the distribution of zeroes of the Jones polynomial VK (t) for a knot K . We have computed numerically the roots of the Jones polynomial for all prime knots with N 6 10 crossings, and found the zeroes scattered about the unit circle |t|=1 with the average distance to the circle approaching a nonzero value as N increases. For torus knots of the type (m; n) we show that all zeroes lie on ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2011
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2011.047