On rectangular HOMFLY for twist knots
نویسندگان
چکیده
منابع مشابه
On Rectangular Diagrams, Legendrian Knots and Transverse Knots
A correspondence is studied in [7] between front projections of Legendrian links in (R, ξstd) and rectangular diagrams. In this paper, we introduce braided rectangular diagrams, and study a relationship with Legendrian links in (R, ξsym). We show Alexander and Markov Theorems for Legendrian links in (R, ξsym). We review a relationship between front projections of Legendrian links in (R, ξstd) a...
متن کاملOn the Reversibility of Twist-spun Knots
Litherland has shown that if a knot is (+)-amphicheiral then its m-twist-spin is reversible. We show that, for classical knots, in many cases the converse holds. The irreversibility (sometimes called noninvertibility) of certain twist-spun knots has been established by Ruberman [10], using the Farber-Levine linking pairing and the Casson-Gordon invariants. More recently, alternative proofs of t...
متن کاملOn Nonabelian Representations of Twist Knots
We study representations of the knot groups of twist knots into SL2(C). The set of nonabelian SL2(C) representations of a twist knot K is described as the zero set in C × C of a polynomial PK(x, y) = QK(y) + xRK(y) ∈ Z[x, y], where x is the trace of a meridian. We prove some properties of PK(x, y). In particular, we prove that PK(2, y) ∈ Z[y] is irreducible over Q. As a consequence, we obtain a...
متن کاملNon–abelian Reidemeister Torsion for Twist Knots
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...
متن کاملTwisted Reidemeister Torsion for Twist Knots
A. The aim of this paper is to give an explicit formula for the SL 2(C)-twisted Reidemeister torsion in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables giving approximations of the twisted Reidemeister torsion for ...
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: Modern Physics Letters A
سال: 2016
ISSN: 0217-7323,1793-6632
DOI: 10.1142/s0217732316502230