The Degree and Branch Set of a Branched Covering.
The Degree of a Map Between Surfaces.
The disjoint curve property.
The Donaldson invariant and embedded 2-spheres.
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The end curve theorem for normal complex surface singularities
We prove the “End Curve Theorem,” which states that a normal surface singularity with rational homology sphere link is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function whose zero set intersects in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” is described by giving an explicit set of equations describing...
The equivariant topological s-cobordism theorem.
The Euler characteristic of a category.
The existence of maps of nonzero degree between aspherical 3-manifolds.
The existence of polar non-degenerate functions on a topological manifold
The extended complexity of three-manifolds.
The extension of Johnson's homomorphism form the Torelli group to the mapping class group.
The Free Loop Space of Globally Symmetric Spaces.
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 fundamental groups of subsets of closed surfaces inject into their first shape groups.
The generalized Schoenflies theorem for absolute suspensions
The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...
The genus of PSl2 (q).
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 Gieseking manifold and its surgery orbifolds.