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Algebraic & Geometric Topology
Article
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arXiv.org e-Print Archive
Preprint . 2002
Data sources: arXiv.org e-Print Archive
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Project Euclid
Other literature type . 2002
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zbMATH Open
Article . 2002
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Algebraic & Geometric Topology
Article . 2002 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2002
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https://dx.doi.org/10.2140/agt...
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https://dx.doi.org/10.2140/agt...
Article
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On Khovanov’s categorification of the Jones polynomial

On Khovanov's categorification of the Jones polynomial
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 21 May 2002Embargo end date: 01 Jan 2002 English Publisher:Mathematical Sciences PublishersJournal:Algebraic & Geometric Topology, volume 2, pages 337-370 (issn: 1472-2747, eissn: 1472-2739, Copyright policy )
Authors: Bar-Natan, Dror;

doi: 10.2140/agt.2002.2.337 , 10.48550/arxiv.math/0201043

arXiv: math/0201043

On Khovanov’s categorification of the Jones polynomial

Abstract

The working mathematician fears complicated words but loves pictures and diagrams. We thus give a no-fancy-anything picture rich glimpse into Khovanov's novel construction of `the categorification of the Jones polynomial'. For the same low cost we also provide some computations, including one that shows that Khovanov's invariant is strictly stronger than the Jones polynomial and including a table of the values of Khovanov's invariant for all prime knots with up to 11 crossings.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-16.abs.html, 34 pages with many figures, source contains associated program and data file

Related Organizations
Keywords

knot invariants, Khovanov, Geometric Topology (math.GT), Invariants of knots and \(3\)-manifolds, Kauffman bracket, Jones polynomial, Mathematics - Geometric Topology, categorification, Mathematics - Quantum Algebra, 57M25, FOS: Mathematics, Knots and links in the \(3\)-sphere, Quantum Algebra (math.QA), Khovanov polynomial

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 240
    popularity
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
240
Top 1%
Top 1%
Top 10%
Green
bronze