Georgia Institute of Technology College of Sciences

Inspired by colored Khovanov homology, for any knot K in the 3-sphere, we define n-colored knot Floer homology as the limit of the cobordism maps from the (full) link Floer homology of the (n,mn)-cable of K to the (full) link Floer homology of  (n,(m+1)n)-cable as m goes to infinity. Colored knot Floer homology is graded by Alexander multi-grading and Maslov grading and it is finite dimensional at each fixed degree. We discuss the module structure of this invariant and overview some examples. This is a joint work with Eugene Gorsky and Beibei Liu.