Infinitely many universally tight contact manifolds with trivial Ozsváth–Szabó contact invariants
نویسندگان
چکیده
Recently Ozsváth and Szabó introduced a new isotopy invariant c(ξ) for contact 3– manifolds (Y, ξ) belonging to the Heegaard Floer homology group ĤF(−Y). They proved [27] that c(ξ) = 0 if ξ is an overtwisted contact structure, and that c(ξ) 6= 0 if ξ is Stein fillable. Later, they introduced also a refined version of the contact invariant denoted by c(ξ) taking values in the so-called Heegaard Floer homology group with twisted coefficients. They proved [24, Theorem 4.2] that c(ξ) 6= 0 if (Y, ξ) is weakly fillable.
منابع مشابه
Infinitely Many Universally Tight Contact Manifolds with Trivial Ozváth–szabó Contact Invariants
In this article we present infinitely many 3–manifolds admitting infinitely many universally tight contact structures each with trivial Ozsváth–Szabó contact invariants. By known properties of these invariants the contact structures constructed in this article are non weakly symplectically fillable.
متن کاملOzsváth-szabó Invariants and Fillability of Contact Structures
Recently, P. Ozsváth and Z. Szabó defined an invariant of contact structures with values in the Heegaard-Floer homology groups. They also proved that the twisted invariant of a weakly symplectically fillable contact structures is non trivial. In this article we prove with an example that their non vanishing result does not hold in general for the untwisted contact invariant. As a consequence of...
متن کاملProduct Formulae for Ozsváth-szabó 4-manifold Invariants
We give formulae for the Ozsváth-Szabó invariants of 4-manifolds X obtained by fiber sum of two manifolds M1, M2 along surfaces Σ1, Σ2 having trivial normal bundle and genus g ≥ 1. The formulae follow from a general result on the Ozsváth-Szabó invariants of the result of gluing two 4-manifolds along a common boundary, which is phrased in terms of relative invariants of the pieces. The fiber sum...
متن کاملHomologie de contact des variétés toröıdales
We show that contact homology distinguishes infinitely many tight contact structures on any orientable, toroidal, irreducible 3–manifold. As a consequence of the contact homology computations, on a very large class of toroidal manifolds, all known examples of universally tight contact structures with nonvanishing torsion satisfy the Weinstein conjecture.
متن کاملComultiplicativity of the Ozsváth-szabó Contact Invariant
Suppose that S is a surface with boundary and that g and h are diffeomorphisms of S which restrict to the identity on the boundary. Let Yg, Yh, and Yh◦g be the threemanifolds with open book decompositions given by (S, g), (S, h), and (S, h ◦ g), respectively. We show that the Ozsváth-Szabó contact invariant is natural under a comultiplication map μ̃ : d HF (−Yh◦g) → d HF (−Yg)⊗ d HF (−Yh). It fo...
متن کامل