Related papers: An involution acting nontrivially on Heegard-Floer…

This paper presents the construction of the Seiberg-Witten-Floer homology of three-manifolds with non-trivial rational homology, and some properties of the invariant of three-manifolds obtained by computing the Euler characteristic. This…

We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We give ncecessary and sufficient conditions for a function defined on the union of the Torelli groups to be an…

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface, instead of Sym^g(Sigma). We then show that the entire invariance proof can be carried…

We prove that a variety of examples of minimal complex surfaces admit exotic diffeomorphisms, providing the first known instances of exotic diffeomorphisms of irreducible 4-manifolds. We also give sufficient conditions for the boundary Dehn…

We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension $2$; in particular, this applies to double branched covers over knots. Our construction gives the Heegaard Floer analogue of Li's…

We give the definition of the Seiberg-Witten-Floer homology group for a homology 3-sphere. Its Euler characteristic number is a Casson-type invariant. For a four-manifold with boundary a homology sphere, a relative Seiberg-Witten invariant…

For any negative definite plumbed 3-manifold M we construct from its plumbed graph a graded Z[U]-module. This, for rational homology spheres, conjecturally equals the Heegaard-Floer homology of Ozsvath and Szabo, but it has even more…

Inspired by the Ozsv\'ath-Szab\'o mixed invariant in ordinary Heegaard Floer theory, we define a mixed invariant $\Phi_{X, \mathfrak{s}}^{I}$ for closed, spin four-manifolds $(X, \mathfrak{s})$ using the cobordism maps on involutive…

In \cite{MR1957829}, Ozsv\'ath and Szab\'o use Heegaard Floer homology to define numerical invariants $d_{1/2}$ and $d_{-1/2}$ for 3-manifolds $Y$ with $H_{1}(Y;\mathbb{Z})\cong \mathbb{Z}$. We define involutive Heegaard Floer theoretic…

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…

The paper describes how known results in Heegaard-Floer homology apply to all known examples of rational blow-downs, and provides several new four dimensional pieces which could be exchanged while preserving some of the Ozsv\'ath-Szab\'o…

We define a notion of Heegaard Floer homology for three dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.

We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured instanton Floer homology theory. To the best of our knowledge, this is the first invariant of contact manifolds -- with or without…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic…

Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(Z), and to a 3-manifold Y with boundary, together with an orientation-preserving diffeomorphism \phi from F to \bdy Y, a module…

Using the Heegaard Floer homology of Ozsvath and Szabo we investigate obstructions to definite intersection pairings bounded by rational homology spheres. As an application we obtain new lower bounds for the four-ball genus of Montesinos…

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 prove that all homology 3-spheres are $J_4$-equivalent, i.e. that any homology 3-sphere can be obtained from one another by twisting one of its Heegaard splittings by an element of the mapping class group acting trivially on the fourth…