Holomorphic discs and sutured manifolds

Holomorphic discs and sutured manifolds

In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds and links. Our invariant is unchanged under product decompositions and is zero for nontaut sutured manifolds. As an application, an invariant of Seifert surfaces is given and is computed in a few i...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

Deformations and Transversality of Pseudo–Holomorphic Discs

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a Banach manifold. MSC: 32H02, 53C15.

Adding 2–handles to Sutured Manifolds

Combinatorial sutured manifold theory is used to study the effects of attaching a 2–handle to an essential simple closed curve on a genus two boundary component of a compact, orientable 3–manifold. The main results concern degenerating handle additions to a simple 3– manifold and essential surfaces in the exterior of a knot or link obtained by “boring” a split link or unknot. (Boring is an oper...

Holomorphic Submersions from Stein Manifolds