  Differential calculus on the space of asymptotically linear curves is
developed. The calculus is applied to the vortex filament equation in its
Hamiltonian description. The recursion operator generating the infinite
sequence of commuting flows is shown to be hereditary. The system is shown to
have a description with a Hamiltonian pair. Master symmetries are found and are
applied to deriving an expression of the constants of motion in involution. The
expression agrees with the inspection of Langer and Perline.
