Narrowing the gap between combinatorial and hyperbolic knot invariants via deep learning

DOI10.1142/S0218216522500031zbMath1497.57004arXiv2204.12885WikidataQ115523464 ScholiaQ115523464MaRDI QIDQ5072603

Daniel Grünbaum

Publication date: 29 April 2022

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.12885

zbMATH Keywords

knot invariantsexploratory data analysisdeep learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Knot theory (57K10) Invariants of 3-manifolds (including skein modules, character varieties) (57K31) Hyperbolic 3-manifolds (57K32)

Uses Software

• SageMath
• NumPy
• SnapPy
• Khoho
• KnotInfo
• TensorFlow
• GitHub

Cites Work

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• The hyperbolic volume of knots from the quantum dilogarithm
• Quantum field theory and the Jones polynomial
• Multilayer feedforward networks are universal approximators
• A categorification of the Jones polynomial
• Deep learning the hyperbolic volume of a knot
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Advancing mathematics by guiding human intuition with AI
• A neural network approach to predicting and computing knot invariants
• Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
• The colored Jones polynomials and the simplicial volume of a knot

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