linguistic:paraphrasing
Braid group

The braid group B is the universal central extension of the modular group, with these sitting as lattices inside the (topological) universal covering group SL (R) → PSL (R). Further, the modular group has a trivial center, and thus the modular group is isomorphic to the quotient group of B modulo its center; equivalently, to the group of inner automorphisms of B.

The braid group B in turn is isomorphic to the knot group of the trefoil knot.