  Fix a suitable link on the disk. Recently, F. Morabito associates each
Hamiltonian symplecticmorphism preserving the link to a braid type. Based on
this construction, Morabito defines a family of pseudometrics on the braid
groups by using the Hofer metric. In this paper, we show that two Hamiltonian
symplecticmorphisms define the same braid type provided that their Hofer
distance is sufficiently small. As a corollary, the pseudometric defined by
Morabito is nondegenerate.
