On the Spectral Sequence from Khovanov Homology to Heegaard Floer Homology

Ozsvath and Szabo ["On the Heegaard Floer homology of branched double-covers." Advances in Mathematics 194, no. 1 (2005): 1-33.] show that there is a spectral sequence the E-2 term of which is (Kh) over tilde (L), and which converges to (HF) over cap(-Sigma(L)). We prove that the E-k term of this spectral sequence is an invariant of the link L for all k >= 2. If L is a transverse link in (S-3,xi(std)), then we show that Plamenevskaya's transverse invariant epsilon(L) gives rise to a transverse invariant, Psi(k)(L), in the E-k term for each k >= 2. We use this fact to compute each term in the spectral sequences associated to the torus knots T(3,4) and T(3,5).