Hyperbolic characteristics on star-shaped hypersurfaces
Infinitely many universally tight contact manifolds with trivial Ozsváth-Szabó contact invariants.
Invariants for Lagrangian tori.
Irreducibility of some representations of the groups of symplectomorphisms and contactomorphisms
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
Knot and braid invariants from contact homology. I.
Lefschetz fibrations, complex structures and Seifert fibrations on .
Lefschetz fibrations on compact Stein surfaces.
Lefschetz pencils and divisors in moduli space.
Legendrian and transverse twist knots
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot with crossing number . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that has exactly Legendrian representatives with maximal Thurston–Bennequin...
Legendrian graphs and quasipositive diagrams
In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on . We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.
Legendrian knots and monopoles.
Maximal Thurston-Bennequin number of two-bridge links.
Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle
We extend the constructions and results of Damian to get topological obstructions to the existence of closed monotone Lagrangian embeddings into the cotangent bundle of a space which is the total space of a fibration over the circle.
On curvature constructions of symplectic forms
We generalize the result of Lerman [Letters Math. Phys. 15 (1988)] concerning the condition of fatness of the canonical connection in a certain principal fibre bundle. We also describe new classes of symplectically fat bundles: twistor budles over spheres, bundles over quaternionic Kähler homogeneous spaces and locally homogeneous complex manifolds.
On iterated torus knots and transversal knots.
On the classification of tight contact structures. I.
On the Heegaard genus of contact 3-manifolds
It is well-known that the Heegaard genus is additive under connected sum of 3-manifolds. We show that the Heegaard genus of contact 3-manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196]) of 3-manifolds, and compute this invariant for some 3-manifolds.
On the number of components of the symplectic representatives of the canonical class
We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.
On the stable equivalence of open books in three-manifolds.
Open books and configurations of symplectic surfaces.