Quasi-isomorphism of grid chain complexes for a connected sum of knots

Abstract

We give a purely combinatorial proof of a Künneth formula for the minus version of knot Floer homology of connected sums by constructing a quasi-isomorphism of grid chain complexes. The quasi-isomorphism naturally deduces that the Legendrian and transverse invariants behave functorially with respect to the connected sum operation.

14 pages, 6 figures