2009/09/28 by Jonathan Fine, Fine, Jonathan
Mathematics · #11G32 (Primary) 14H57 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA #msc:11G32 #msc:14H57
paper · pdf · doi:10.48550/arxiv.0909.5197
3 pages, no figures
arxiv created 2009/09/28 · arxiv updated 2009/12/01
A Bely\uı pair is a holomorphic map from a Riemann surface to S2 with additional properties. A dessin d'enfants is a bipartite graph with additional structure. It is well know that there is a bijection between Belyĭ 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\uı pairs, and another on dessin d'enfants. We ask if the two definitions give the same filtration.