The spin refined Kauffman bracket skein module ofS 1×S 2 and lens spaces

1996 ◽  
Vol 91 (1) ◽  
pp. 495-509 ◽  
Author(s):  
Gregor Masbaum
Keyword(s):  
Lens Spaces ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module

scholarly journals On the KBSM of links in lens spaces

2018 ◽  
Vol 27 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Boštjan Gabrovšek ◽  
Enrico Manfredi
Keyword(s):  
Lens Spaces ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Kauffman Bracket Skein Module ◽  
Interesting Class

In this paper, the properties of the Kauffman bracket skein module (KBSM) of [Formula: see text] are investigated. Links in lens spaces are represented both through band and disk diagrams. The possibility to transform between the diagrams enables us to compute the KBSM on an interesting class of examples consisting of inequivalent links with equivalent lifts in the [Formula: see text]-sphere. The computations show that the KBSM is an essential invariant, that is, it may take different values on links with equivalent lifts. We also show how the invariant is related to the Kauffman bracket of the lift in the [Formula: see text]-sphere.

scholarly journals KAUFFMAN BRACKET SKEIN MODULE OF THE CONNECTED SUM OF TWO PROJECTIVE SPACES

2011 ◽  
Vol 20 (05) ◽  
pp. 651-675 ◽  
Author(s):  
MACIEJ MROCZKOWSKI
Keyword(s):  
Projective Spaces ◽  
Lens Spaces ◽  
Connected Sum ◽  
Skein Module ◽  
Kauffman Bracket ◽  
Reidemeister Moves ◽  
Kauffman Bracket Skein Module

Diagrams and Reidemeister moves for links in a twisted S1-bundle over an unorientable surface are introduced. Using these diagrams, we compute the Kauffman Bracket Skein Module (KBSM) of ℝP3♯ℝP3. In particular, we show that it has torsion. We also present a new computation of the KBSM of S1 × S2 and the lens spaces L(p, 1).

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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