scholarly journals On the colored Jones polynomial, sutured Floer homology, and knot Floer homology

2010 ◽  
Vol 223 (6) ◽  
pp. 2114-2165 ◽  
Author(s):  
J. Elisenda Grigsby ◽  
Stephan M. Wehrli
Keyword(s):  
Floer Homology ◽  
Jones Polynomial ◽  
Colored Jones Polynomial ◽  
Knot Floer Homology

THE COLORED JONES POLYNOMIALS OF DOUBLES OF KNOTS

2008 ◽  
Vol 17 (08) ◽  
pp. 925-937
Author(s):  
TOSHIFUMI TANAKA
Keyword(s):  
Jones Polynomial ◽  
Colored Jones Polynomial ◽  
Volume Conjecture ◽  
Jones Polynomials ◽  
Skein Theory ◽  
Colored Jones Polynomials

We give formulas for the N-colored Jones polynomials of doubles of knots by using skein theory. As a corollary, we show that if the volume conjecture for untwisted positive (or negative) doubles of knots is true, then the colored Jones polynomial detects the unknot.

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

scholarly journals Stability properties of the colored Jones polynomial

2019 ◽  
Vol 28 (08) ◽  
pp. 1950050
Author(s):  
Christine Ruey Shan Lee
Keyword(s):  
Power Series ◽  
Jones Polynomial ◽  
Topological Information ◽  
Colored Jones Polynomial ◽  
Stability Properties ◽  
Link Complement

It is known that the colored Jones polynomial of a [Formula: see text]-adequate link has a well-defined tail consisting of stable coefficients, and that the coefficients of the tail carry geometric and topological information on the [Formula: see text]-adequate link complement. We show that a power series similar to the tail of the colored Jones polynomial for [Formula: see text]-adequate links can be defined for all links, and that it is trivial if and only if the link is non [Formula: see text]-adequate.

scholarly journals An introduction to knot Floer homology and curved bordered algebras

2020 ◽  
Vol 80 (2) ◽  
pp. 211-236
Author(s):  
Antonio Alfieri ◽  
Jackson Van Dyke
Keyword(s):  
Floer Homology ◽  
Knot Floer Homology

scholarly journals Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

2008 ◽  
Vol 2008 ◽  
Author(s):  
Kenneth L. Baker ◽  
J. Elisenda Grigsby ◽  
Matthew Hedden
Keyword(s):  
Floer Homology ◽  
Lens Spaces ◽  
Knot Floer Homology ◽  
Grid Diagrams

scholarly journals A combinatorial spanning tree model for knot Floer homology

2012 ◽  
Vol 231 (3-4) ◽  
pp. 1886-1939 ◽  
Author(s):  
John A. Baldwin ◽  
Adam Simon Levine
Keyword(s):  
Spanning Tree ◽  
Floer Homology ◽  
Tree Model ◽  
Knot Floer Homology

scholarly journals DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

2004 ◽  
Vol 15 (09) ◽  
pp. 959-965 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Difference Equation ◽  
Jones Polynomial ◽  
Order Difference ◽  
Colored Jones Polynomial ◽  
First Order ◽  
Torus Knot ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Hypergeometric Type ◽  
The Difference

We prove that the N-colored Jones polynomial for the torus knot [Formula: see text] satisfies the second order difference equation, which reduces to the first order difference equation for a case of [Formula: see text]. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for [Formula: see text].

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