Torus links and colored Heegaard Floer homology

For any knot K in the three-sphere, we define new knot invariants labeled by integers which are invariant under full twists. These invariants, called colored Heegaard Floer homology of K, is the colimit of the cobordism maps from the (n, mn)-cable of K to (n, (m+1)n)-cable by letting m goes to infinity. We will focus on the explicit computation of colored Heegaard Floer homology for the family of L-space knots, particularly for unknots from their Alexander polynomials.