English

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 S2S^2 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.

Keywords

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