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

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 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].

scholarly journals The Torelli group and the Kauffman bracket skein module

2017 ◽  
Vol 165 (1) ◽  
pp. 163-178
Author(s):  
SHUNSUKE TSUJI
Keyword(s):  
Torelli Group ◽  
Oriented Surface ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module ◽  
New Construction

AbstractWe introduce an embedding of the Torelli group of a compact connected oriented surface with non-empty connected boundary into the completed Kauffman bracket skein algebra of the surface, which gives a new construction of the first Johnson homomorphism.

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