arXiv subjects
Publications and source records attributed to Paolo Ghiggini.
We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology. The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient manifold.
We define a relative version of contact homology for contact manifolds with convex boundary, and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.
In this article we present infinitely many 3-manifolds admitting infinitely many universally tight contact structures each with trivial Ozsvath-Szabo contact invariants. By known properties of these invariants the contact structures constructed here are non weakly symplectically fillable.
We explain the effect of applying a full Lutz twist along a pre-Lagrangian torus in a contact 3-manifold, on the contact invariant in Heegaard Floer homology with twisted coefficients.
We prove that the Ozsvath-Szabo contact invariant of a closed contact 3-manifold with positive Giroux torsion vanishes.
We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.
Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai's theory of sutured manifold decomposition and contact topology. We implement this strategy for genus-one knots, obtaining as a corollary that, if rational surgery on a knot $K$ gives the Poincare homology sphere $Σ(2,3,5)$, then $K$ is the left-handed trefoil knot.
We classify tight contact structures on the small Seifert fibered 3--manifold M(-1; r_1, r_2, r_3) with r_i in (0,1) and r_1, r_2 \geq 1/2. The result is obtained by combining convex surface theory with computations of contact Ozsvath--Szabo invariants. We also show that some of the tight contact structures on the manifolds considered are nonfillable, justifying the use of Heegaard Floer theory.
We use the Ozsvath-Szabo contact invariant to produce examples of strongly symplectically fillable contact 3-manifolds which are not Stein fillable.
In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.
In this article we provide an infinite family of weakly symplectically fillable contact structures with trivial Ozsvath-Szabo contact invariants over Z/2Z. As a consequence of this fact, we show how Heegaard-Floer theory can distinguish between weakly and strongly fillable contact structures.
We classify positive, tight contact structures on closed Seifert fibered 3-manifolds with base S^2, three singular fibers and e_0\geq 0.
Using convex surfaces and Kanda's classification theorem, we classify Legendrian isotopy classes of Legendrian linear curves in all tight contact structures on $T^3$. Some of the knot types considered in this article provide new examples of non transversally simple knot types.