Big data approaches to knot theory: Understanding the structure of the Jones polynomial
From MaRDI portal
Publication:5057321
DOI10.1142/S021821652250095XMaRDI QIDQ5057321
Radmila Sazdanovic, Mustafa Hajij, Jesse Levitt
Publication date: 16 December 2022
Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.10086
signaturedata analysisJones polynomialknot invariantsPCAtopological data analysisknot polynomialsfiltered PCA
Statistical aspects of big data and data science (62R07) Knot polynomials (57K14) Knot theory (57K10) Topological data analysis (62R40)
Uses Software
Cites Work
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- The tail of a quantum spin network
- The Bailey chain and mock theta functions
- The colored Jones polynomial of singular knots
- \(q\)-series and tails of colored Jones polynomials
- Khovanov homology and the slice genus
- The hyperbolic volume of knots from the quantum dilogarithm
- The colored Jones polynomial and the \(A\)-polynomial of knots
- Classification of knot projections
- The Yang-Baxter equation and invariants of links
- The first 1,701,936 knots
- A trivial tail homology for non-\(A\)-adequate links
- Ribbon graphs and their invariants derived from quantum groups
- Topological persistence and simplification
- On the Melvin-Morton-Rozansky conjecture
- Integrality and symmetry of quantum link invariants
- Deep learning the hyperbolic volume of a knot
- Pretzel knots and \(q\)-series
- The colored Jones function is \(q\)-holonomic
- The head and tail of the colored Jones polynomial for adequate knots
- The colored Kauffman Skein relation and the head and tail of the colored Jones polynomial
- An Introduction to the Volume Conjecture
- On the AJ conjecture for knots
- A PARTIAL ORDERING OF KNOTS AND LINKS THROUGH DIAGRAMMATIC UNKNOTTING
- The growth of the number of prime knots
- A polynomial time knot polynomial
- Foundations of the Colored Jones Polynomial of singular knots
- Knot fertility and lineage
- Verification of the Jones unknot conjecture up to 22 crossings
- Twist regions and coefficients stability of the colored Jones polynomial
- CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL
- Verification of the Jones unknot conjecture up to 24 crossings
- A neural network approach to predicting and computing knot invariants
- On the head and the tail of the colored Jones polynomial
- Natural classification of knots
- The colored Jones polynomials and the simplicial volume of a knot