An introduction to categorifying quantum knot invariants

Webster, Ben

doi:10.2140/gtm.2012.18.253

Cited by 5 publications

(5 citation statements)

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“…Categorification of link invariants has been a source of fruitful interactions between physics and low dimensional topology over the past decades (see [10,22,30] for reviews). Since the advent of the Khovanov homology [17], which categorifies the Jones polynomials of links, there has been constructions of other homological theories, for example, knot Floer homology [23,26], Khovanov-Rozansky homology [18] and HOMFLY homology [19] that categorify the well-known link polynomials: Alexander, sl(N )-invariants and HOMFLY polynomial, respectively.…”

Section: Introductionmentioning

confidence: 99%

Knot Complement, ADO Invariants and their Deformations for Torus Knots

Chae

2020

SIGMA

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A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of ADO3 polynomial of torus knots is provided.

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Section: Introductionmentioning

confidence: 99%

Knot Complement, ADO Invariants and their Deformations for Torus Knots

Chae

2020

SIGMA

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“…Categorification of link invariants has been a source of fruitful interactions between physics and low dimensional topology over the past decades (see [31,32,33] for reviews). Since the advent of the Khovanov homology [17], which categorifies the Jones polynomials of links, there has been constructions of other homological theories, for example, knot Floer homology [18,19], Khovanov-Rozansky homology [20] and HOMFLY homology [21] that categorify the well-known link polynomials, Alexander, sl(N )-invariants and HOMFLY polynomial, respectively.…”

Section: Introductionmentioning

confidence: 99%

Knot Complement, ADO-Invariants and their Deformations for Torus Knots

Chae

2020

Preprint

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A relation between the two-variable series knot invariant and the Akutus-Deguchi-Ohtsuki(ADO)invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for certain ADO-invariants of torus knots obtained from the series invariant of complement of a knot. Furthermore, one parameter deformation of ADO 3 -polynomial of torus knots is provided. CONTENTS 4 Appendix 132 Background Two-Variable Series Knot ComplementA series invariant F K for a complement of a knot M 3 K was introduced [1]. It has various properties such as the gluing formula and the (Dehn) surgery formula. This knot invariant F K

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“…There are plenty of actions of the braid groups which are now know, in particular with their connections to higher representation theory and link homologies. We mention here a couple of them in an non-exhaustive manner: Deligne [Del97], Seidel-Thomas [ST01], Khovanov [Kho02], Stroppel [Str05], Mazorchuk-Stroppel [MS05,MS07], Rouquier [Rou06], Khovanov-Rozansky [KR08], Webster [Web12], Cautis-Kamnitzer [CK12], Lipshitz-Ozsvath-Thurston [LOT13]... Many of them are known to be faithful.…”

Section: Introductionmentioning

confidence: 99%