We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a consequence, we show that the Eliashberg-Chekanov twist knots E_n are not transversely simple for n odd and n>3.
We show that every 3--manifold admits a Heegaard diagram in which a truncated version of Heegaard Floer homology (when the holomorpic disks pass through the basepoints at most once) can be computed combinatorially.
We describe an invariant of links in the three-sphere which is closely related to Khovanovs Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanovs definition with an exterior algebra. The two invariants have
the same reduction modulo 2, but differ over the rationals. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones polynomial.
The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $HFm$. Moreover, a complete argument is also given purely within the realm of grid diagrams.
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.
