The Approximation of Instantons.
The Canonical Class and the Properties of Kähler Surfaces.
The deformation theory of anti-self-dual conformal structures.
The Donaldson invariant and embedded 2-spheres.
The Fukumoto-Furuta and the Ozsváth-Szabó invariants for spherical 3-manifolds
We show that the Fukumoto-Furuta invariant for a rational homology 3-sphere M, which coincides with the Neumann-Siebenmann invariant for a Seifert rational homology 3-sphere, is the same as the Ozsváth-Szabó's correction term derived from the Heegaard Floer homology theory if M is a spherical 3-manifold.
The geography of simply-connected symplectic manifolds
By using the Seiberg-Witten invariant we show that the region under the Noether line in the lattice domain is covered by minimal, simply connected, symplectic 4-manifolds.
The geometry of the Seiberg-Witten invariants.
The Novikov conjecture and low-dimensional topology.
The Seiberg-Witten invariants and 4-manifolds with essential tori.
The Seiberg-Witten invariants of symplectic four-manifolds
The Smith Conjecture in dimension four and equivariant gauge theory.
The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on .
The volume spectrum of hyperbolic 4-manifolds.
The Yang-Mills equations and the topology of 4-manifolds
Topological Classification of 4-Dimensional Complete Intersections.
Topological manifolds and real algebraic geometry
We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological -manifolds.