Deep learning the hyperbolic volume of a knot

High Energy Physics - Theory Physics QC1-999 FOS: Physical sciences Geometric Topology (math.GT) 01 natural sciences Mathematics - Geometric Topology High Energy Physics - Theory (hep-th) Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics
DOI: 10.1016/j.physletb.2019.135033 Publication Date: 2019-10-28T16:27:39Z
ABSTRACT
18 pages, 9 figures, updated figures<br/>An important conjecture in knot theory relates the large-$N$, double scaling limit of the colored Jones polynomial $J_{K,N}(q)$ of a knot $K$ to the hyperbolic volume of the knot complement, $\text{Vol}(K)$. A less studied question is whether $\text{Vol}(K)$ can be recovered directly from the original Jones polynomial ($N = 2$). In this report we use a deep neural network to approximate $\text{Vol}(K)$ from the Jones polynomial. Our network is robust and correctly predicts the volume with $97.6\%$ accuracy when training on $10\%$ of the data. This points to the existence of a more direct connection between the hyperbolic volume and the Jones polynomial.<br/>
SUPPLEMENTAL MATERIAL
Coming soon ....
REFERENCES (33)
CITATIONS (30)
EXTERNAL LINKS
PlumX Metrics
RECOMMENDATIONS
FAIR ASSESSMENT
Coming soon ....
JUPYTER LAB
Coming soon ....