scholarly journals ON THE KAUFFMAN BRACKET SKEIN MODULE OF THE QUATERNIONIC MANIFOLD

2007 ◽  
Vol 16 (01) ◽  
pp. 103-125 ◽  
Author(s):  
PATRICK M. GILMER ◽  
JOHN M. HARRIS
Keyword(s):  
Cyclotomic Polynomials ◽  
Quantum Invariants ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Linearly Independent ◽  
Quaternionic Manifold ◽  
Kauffman Bracket Skein Module ◽  
Five Elements

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over ℤ[A±1] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the ℤ2-homology of the manifold, we determine that they are linearly independent.

scholarly journals The Bubble skein element and applications

2014 ◽  
Vol 23 (14) ◽  
pp. 1450076 ◽  
Author(s):  
Mustafa Hajij
Keyword(s):  
Jones Polynomial ◽  
Colored Jones Polynomial ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Linearly Independent ◽  
Kauffman Bracket Skein Module ◽  
Marked Points

We study a certain skein element in the relative Kauffman bracket skein module of the disk with some marked points, and expand this element in terms of linearly independent elements of this module. This expansion is used to compute and study the head and the tail of the colored Jones polynomial and in particular we give a simple q-series for the tail of the knot 85. Furthermore, we use this expansion to obtain an easy determination of the theta coefficients.

The Kauffman bracket skein module ofS 1×S 2

1995 ◽  
Vol 220 (1) ◽  
pp. 65-73 ◽  
Author(s):  
Jim Hoste ◽  
Józef H. Przytycki
Keyword(s):  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module

THE CHARACTER VARIETY OF A FAMILY OF ONE-RELATOR GROUPS

2012 ◽  
Vol 23 (01) ◽  
pp. 1250015 ◽  
Author(s):  
KHALED QAZAQZEH
Keyword(s):  
Character Variety ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module ◽  
One Relator Groups

We prove that the character variety of a family of one-relator groups has only one defining polynomial and we provide the means to compute it. Consequently, we give a basis for the Kauffman bracket skein module of the exterior of the rational link Lp/q of two components modulo the (A + 1)-torsion.

scholarly journals The Yang-Mills measure in the Kauffman bracket skein module

2003 ◽  
Vol 78 (1) ◽  
pp. 1-17 ◽  
Author(s):  
D Bullock ◽  
Joanna Kania-Bartoszynska ◽  
Charles Frohman
Keyword(s):  
Yang Mills ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module

scholarly journals Categorification of the Kauffman bracket skein module ofI–bundles over surfaces

2004 ◽  
Vol 4 (2) ◽  
pp. 1177-1210 ◽  
Author(s):  
Marta M Asaeda ◽  
Jozef H Przytycki ◽  
Adam S Sikora
Keyword(s):  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module

scholarly journals The Kauffman bracket skein module of the handlebody of genus 2 via braids

2019 ◽  
Vol 28 (13) ◽  
pp. 1940020
Author(s):  
Ioannis Diamantis
Keyword(s):  
Intermediate Step ◽  
Infinite Matrix ◽  
Natural Basis ◽  
Skein Modules ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module ◽  
Genus 2 ◽  
Lower Triangular ◽  
Invertible Elements

In this paper we present two new bases, [Formula: see text] and [Formula: see text], for the Kauffman bracket skein module of the handlebody of genus 2 [Formula: see text], KBSM[Formula: see text]. We start from the well-known Przytycki-basis of KBSM[Formula: see text], [Formula: see text], and using the technique of parting we present elements in [Formula: see text] in open braid form. We define an ordering relation on an augmented set [Formula: see text] consisting of monomials of all different “loopings” in [Formula: see text], that contains the sets [Formula: see text], [Formula: see text] and [Formula: see text] as proper subsets. Using the Kauffman bracket skein relation we relate [Formula: see text] to the sets [Formula: see text] and [Formula: see text] via a lower triangular infinite matrix with invertible elements in the diagonal. The basis [Formula: see text] is an intermediate step in order to reach at elements in [Formula: see text] that have no crossings on the level of braids, and in that sense, [Formula: see text] is a more natural basis of KBSM[Formula: see text]. Moreover, this basis is appropriate in order to compute Kauffman bracket skein modules of closed–connected–oriented (c.c.o.) 3-manifolds [Formula: see text] that are obtained from [Formula: see text] by surgery, since isotopy moves in [Formula: see text] are naturally described by elements in [Formula: see text].

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