The existence of algebraic surfaces with preassigned Chern numbers.
The existence of critical values in an abstract perturbation problem.
The existence of polar non-degenerate functions on a topological manifold
The extension of Johnson's homomorphism form the Torelli group to the mapping class group.
The First Cohomology Group of Leaves and Local Stability of Compact Foliations.
The flow completion of a manifold with vector field.
The Fujiki class and positive degree maps
We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.
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 geometric genus of hypersurface singularities
Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all superisolated and Newton non-degenerate hypersurface singularities.
The geometry of a vector bundle endowed with a cone field.
The Geometry of Critical and Near-Critical Values of Differentiable Mappings.
The geometry of -covered foliations.
The geometry of Teichmüller space via geodesic currents.
The geometry of the local cohomology filtration in equivariant bordism.
The geometry of the Seiberg-Witten invariants.
The Gromov invariant and the Donaldson-Smith standard surface count.
The Gromov width of complex Grassmannians.
The Group of Large Diffeomorphisms in General Relativity
We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
The Hauptvermutung for homeomorphisms II. A proof valid for open 4-manifolds
The height of the first Stiefel-Whitney class of any nonorientable real flag manifold