A characterization of osculating maps
A compendium of pseudoholomorphic beasts in .
A non-abelian Seiberg-Witten invariant for integral homology 3-spheres.
A note on trignometric sums arising in gauge theory.
A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of connections.
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 exotic smooth structure on .
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 infinite family of tight, not semi-fillable contact three-manifolds.
Analytic Surgery and the Eta Invariant.
ASD moduli spaces over four-manifolds with tree-like ends.
Circle-valued Morse theory and Reidemeister torsion.
Construction de sous-variétés symplectiques
Correction to “Properties of pseudoholomorphic curves in symplectisations. I : asymptotics”
Diffeomorphisms, symplectic forms and Kodaira fibrations.
Einstein manifolds, volume rigidity and Seiberg-Witten theory
Einstein metrics and smooth structures.
Equivariant Floer groups for binary polyhedral spaces.
Floer homology of surgeries on two-bridge knots.
Gauge theoretical methods in the classification of non-Kählerian surfaces
The classification of class VII surfaces is a very difficult classical problem in complex geometry. It is considered by experts to be the most important gap in the Enriques-Kodaira classification table for complex surfaces. The standard conjecture concerning this problem states that any minimal class VII surface with b₂ > 0 has b₂ curves. By the results of [Ka1]-[Ka3], [Na1]-[Na3], [DOT], [OT] this conjecture (if true) would solve the classification problem completely. We explain a new approach...