2025/09/17 by Faye Jackson, Jackson, Faye · 1 citation
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2509.14454
Given an elliptic fibration π: M → S2 with singular locus Δ⊆ S2, let Br(π) < Mod(S2,Δ) be the subgroup of the spherical braid group consisting of those braids that lift to a fiber-preserving diffeomorphism of M. We classify the order n = |Δ| elements of Br(π) up to conjugacy in Br(π). To do so, we relate these conjugacy classes to special points on the SL2-character variety for (S2,Δ) that correspond naturally to the exceptional elliptic curves ℂ/ℤ[ω] and ℂ/ℤ[i] with their associated norms on ℤ[ω] and ℤ[i]. We also show that there are no elements of order n-1 or n-2 in Br(π), as there are in Mod(S2,Δ).