  In this paper we determine all possible cohomological invariants of
Aut(J)-torsors in Galois cohomology with mod 2 coefficients (characteristic of
the base field not 2), for J a split central simple Jordan algebra of odd
degree n>=3. This has already been done for J of orthogonal and exceptional
type, and we extend these results to unitary and symplectic type. We will use
our results to compute the essential dimensions of some groups, for example we
show that ed(PSp(2n))=n+1 for n odd.
