Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Khovanov Laplacian and Khovanov Dirac for knots and links
View through CrossRef
Abstract
Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology.
Title: Khovanov Laplacian and Khovanov Dirac for knots and links
Description:
Abstract
Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000.
This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams.
The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology.
Related Results
Comparative Study of Tensile Strength in Vicryl™ vs. Prolene™ 5-0 Knots: Impact of Throw Type and Count
Comparative Study of Tensile Strength in Vicryl™ vs. Prolene™ 5-0 Knots: Impact of Throw Type and Count
Abstract
Background
Knots are the weakest point of sutures, making their security and tensile strength critical. While suture ma...
The Khovanov homology of knots
The Khovanov homology of knots
<p>The Khovanov homology is a knot invariant which first appeared in Khovanov's original paper of 1999, titled ``a categorification of the Jones polynomial.'' This thesis aim...
Estimations uniformes pour des problèmes de transmission à changement de signe : Liens avec les triplets de frontière et la quantification de l’incertitude
Estimations uniformes pour des problèmes de transmission à changement de signe : Liens avec les triplets de frontière et la quantification de l’incertitude
Présentation du domaine: Il s'agit d'étudier des opérateurs différentiels sur des variétés riemanniennes singulières et leurs applications. Parmi les opérateurs les plus importants...
A note on Khovanov–Rozansky sl2-homology and ordinary Khovanov homology
A note on Khovanov–Rozansky sl2-homology and ordinary Khovanov homology
In this paper we present an explicit isomorphism between Khovanov–Rozansky sl2-homology and ordinary Khovanov homology. This result was originally claimed in Khovanov and Rozansky'...
Spanning trees and Khovanov homology
Spanning trees and Khovanov homology
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show that there exists a complex generated by the...
Electrical stress of graphene field effect transistor under different bias voltages Reliability studies
Electrical stress of graphene field effect transistor under different bias voltages Reliability studies
In this paper, graphene field effect transistors (GFET) with the top-gate structure are taken as the research object. Conducted electrical stress reliability studies under differen...
The spectrum and metric dimension of Indu–Bala product of graphs
The spectrum and metric dimension of Indu–Bala product of graphs
Given a connected graph [Formula: see text], the distance Laplacian matrix [Formula: see text] is defined as [Formula: see text], and the distance signless Laplacian matrix [Formul...
On knots in overtwisted contact structures
On knots in overtwisted contact structures
We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cas...