A class of tight contact structures on .
A compendium of pseudoholomorphic beasts in .
A few remarks about symplectic filling.
A Legendrian Thurston-Bennequin bound from Khovanov homology.
A stable classification of Lefschetz fibrations.
A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds
In this paper we show that given any 3-manifold and any non-fibered class in there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.
An index inequality for embedded pseudoholomorphic curves in symplectizations
Let be a surface with a symplectic form, let be a symplectomorphism of , and let be the mapping torus of . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in , with cylindrical ends asymptotic to periodic orbits of or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand...
An inequality for symplectic fillings of the link of a hypersurface K3 singularity
Some relations between normal complex surface singularities and symplectic fillings of the links of the singularities are discussed. For a certain class of singularities of general type, which are called hypersurface K3 singularities in this paper, an inequality for numerical invariants of any minimal symplectic fillings of the links of the singularities is derived. This inequality can be regarded as a symplectic/contact analog of the 11/8-conjecture in 4-dimensional topology.
An infinite family of tight, not semi-fillable contact three-manifolds.