A filtration question on Belyi pairs and dessins
Algebraic Geometry
2009-09-30 v1 Quantum Algebra
Abstract
A Bely\u{\i} pair is a holomorphic map from a Riemann surface to with additional properties. A dessin d'enfants is a bipartite graph with additional structure. It is well know that there is a bijection between Bely\u{i} pairs and dessins d'enfants. Vassiliev has defined a filtration on formal sums of isotopy classes of knots. Motivated by this, we define a filtration on formal sums of Bely\u{\i} pairs, and another on dessin d'enfants. We ask if the two definitions give the same filtration.
Cite
@article{arxiv.0909.5197,
title = {A filtration question on Belyi pairs and dessins},
author = {Jonathan Fine},
journal= {arXiv preprint arXiv:0909.5197},
year = {2009}
}
Comments
3 pages, no figures