THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS
نویسندگان
چکیده
منابع مشابه
The Non-commutative A-polynomial of Twist Knots
The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form J(n) = P k c(n, k)Ĵ(k) given a recursion relation for (Ĵ(n)) a the hyp...
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In [6] Mora described an algorithm which, if it terminates, returns a noncommutative Gröbner basis. Here we follow that paper to prove the correctness of the algorithm as implemented by Dié Gijsbers and the author in GAP, cf. [1]. The algorithm is the core algorithm of the GAP package GBNP for computing with non-commutative polynomials. Earlier versions of this section were written with the hel...
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Twist knots form a family of special two–bridge knots which include the trefoil knot and the figure eight knot. The knot group of a two–bridge knot has a particularly nice presentation with only two generators and a single relation. One could find our interest in this family of knots in the following facts: first, twist knots except the trefoil knot are hyperbolic; and second, twist knots are n...
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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...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2010
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s021821651000856x