Geometric subgroups of surface braid groups

Abstract

Let M be a surface, let N be a subsurface, and let n≤m be two positive integers. The inclusion of N in M gives rise to a homomorphism from the braid group B n N with n strings on N to the braid group B m M with m strings on M. We first determine necessary and sufficient conditions that this homomorphism is injective, and we characterize the commensurator, the normalizer and the centralizer of π 1 N in π 1 M. Then we calculate the commensurator, the normalizer and the centralizer of B n N in B m M for large surface braid groups.

Locations

• French digital mathematics library (Numdam) - View - PDF
• Annales de l’institut Fourier - View - PDF