Linking number of modular knots
Dynamical Systems
2023-01-31 v2 Geometric Topology
Number Theory
Abstract
We compute the linking number of two modular knots in the space with the trefoil filled in, which answers a question posed by Ghys in 2007. This computation is realized through the correspondence between modular links and Lorenz links, and can be thought of as an intersection number involving Conway topographs. We compare this to a second formula for the linking number of Lorenz links, which was proven by Stephen F. Kennedy in 1994.
Keywords
Cite
@article{arxiv.2301.01334,
title = {Linking number of modular knots},
author = {James Rickards},
journal= {arXiv preprint arXiv:2301.01334},
year = {2023}
}
Comments
The main results were also proven by Christopher-Lloyd Simon in his thesis and in arxiv:2211.05957, and precedence should go to his work. See the author's note (section 0) for more details