  We compute the Chekanov-Eliashberg contact homology of what we call the
Legendrian closure of a positive braid. We also construct an augmentation for
each such link diagram. Then we apply the monodromy techniques established in
an earlier paper to a certain natural loop in the space L' of positive
Legendrian (p,q) torus knots to show that L' has a nontrivial fundamental
group, which is mapped non-injectively into the fundamental group of K by the
map induced by inclusion (here, K is the space of all smooth positive (p,q)
torus knots). This is the first example that Legendrian and classical knots
behave differently at the level of one parameter families.
