Related papers: Action of the cork twist on Floer homology
We make use of the action of $H_1(Y)$ in Heegaard Floer homology to generalize the Ozsv\'ath-Szab\'o correction terms for $3$-manifolds with standard $\operatorname{HF}^\infty$. We establish the basic properties of these invariants:…
Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a…
Ozsvath and Szabo gave a combinatorial description of knot Floer homology based on a cube of resolutions, which uses maps with twisted coefficients. We study the t=1 specialization of their construction. The associated spectral sequence…
Ozsvath and Szabo proved that knot Floer homology determines the genera of knots in S^3. We will generalize this deep result to links in homology 3-spheres, by adapting their method. Our proof relies on a result of Gabai and some…
We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they…
We show that, for each integer n, there exist infinitely many pairs of n-framed knots representing homeomorphic but non-diffeomorphic (Stein) 4-manifolds, which are the simplest possible exotic 4-manifolds regarding handlebody structures.…
Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for…
We establish some general relations between Heegaard Floer based contact invariants. In particular, we observe that if the contact invariant of large negative, respectively positive, contact surgeries along a Legendrian knot does not…
We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein…
It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of $K$ detects more structure of minimal genus Seifert surfaces for $K$. We define an invariant of…
We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to…
We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These "relative adjunction inequalities" improve the adjunction inequalities for closed surfaces which have been…
We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose…
Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a certain three-manifold invariant, Heegaard Floer homology,…
The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic…
We recently defined an invariant of contact manifolds with convex boundary in Kronheimer and Mrowka's sutured monopole Floer homology theory. Here, we prove that there is an isomorphism between sutured monopole Floer homology and sutured…
We use Khovanov-Rozansky gl(N) link homology to define invariants of oriented smooth 4-manifolds, as skein modules constructed from certain 4-categories with well-behaved duals. The technical heart of this construction is a proof of the…
We establish a criterion that ensures a bounded almost complex curve in a bounded almost complex 4-manifold minimizes genus amongst all smooth surfaces that share its homology class and the transverse link on its boundary. An immediate…
The main goal of the present article is the computation of the Heegaard Floer homology introduced by Ozsvath and Szabo for a family of plumbed rational homology 3-spheres. The main motivation is the study of the Seiberg-Witten type…
Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$…