Related papers: On binding sums of contact manifolds

We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.

We explore the Fourier transform of the Heegaard Floer $d$-invariants, which is particularly well-behaved with respect to connected sum. As corollaries, we show that lens spaces are cancellable in the monoid of 3-manifolds up to integer…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a…

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2)…

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other…

We construct open symplectic manifolds which are convex at infinity ("Liouville manifolds") and which are diffeomorphic, but not symplectically isomorphic, to cotangent bundles T^*S^{n+1}, for any n+1 \geq 3. These manifolds are constructed…

We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition…

We study several aspects of fillings for links of general quotient singularities using Floer theory, including co-fillings, Weinstein fillings, strong fillings, exact fillings and exact orbifold fillings, focusing on non-existence of exact…

Associated to an embedded surface in the $3$-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, wherefrom we deduce complete invariants of handlebody links, tunnels of handlebody links, and…

In this paper, we show that the Ozsv\'ath-Szab\'o contact invariant $c^+(\xi)\in HF^+(-Y)$ of a contact 3-manifold $(Y,\xi)$ can be calculated combinatorially if $Y$ is the boundary of a certain type of plumbing $X$, and $\xi$ is induced by…

For any asymptotically dynamically convex contact manifold $Y$, we show that $SH_*(W)=0$ is a property independent of the choice of topologically simple (i.e.\ $c_1(W)=0$ and $\pi_{1}(Y)\rightarrow \pi_1(W)$ is injective) Liouville filling…

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…

We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…

In this paper, we determine the group of contact transformations modulo contact isotopies for Legendrian circle bundles over closed surfaces of nonpositive Euler characteristic. These results extend and correct those presented by the first…

We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the…

The search for classical or quantum combinatorial invariants of compact n-dimensional manifolds (n=3,4) plays a key role both in topological field theories and in lattice quantum gravity. We present here a generalization of the partition…

We characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. We also show that for this class of 3-manifolds the existence of Stein fillings is equivalent to the existence of symplectic…

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

In this paper, we shall prove that any Heegaard splitting of a $\partial$-reducible 3-manifold $M$, say $M=W\cup V$, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings…