Let $M$ be a surface, let $N$ be a subsurface, and let $n\le m$ 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 ${\pi }_{1}N$ in ${\pi }_{1}M$. Then we calculate the commensurator, the normalizer and the centralizer of $B_{n}N$ in $B_{m}M$ for large surface braid...

On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.