We discuss several applications of Seiberg-Witten theory in conjunction with an embedding theorem (proved elsewhere) for complex 2-dimensional Stein manifolds with boundary. We show that a closed, real 2-dimensional surface smoothly embedded in the interior of such a manifold satisfies an adjunction inequality, regardless of the sign of its self-intersection. This inequality gives constraints on the minimum genus of a smooth surface representing a given 2-homology class. We also discuss consequences for the contact structures existing on the boundaries of these Stein manifolds. We prove a slice version of the Bennequin-Eliashberg inequality for holomorphically fillable contact structures, and we show that there exist families of homology 3-spheres with arbitrarily large numbers of homotopic, nonisomorphic tight contact structures, Another result we mention is that the canonical class of a complex 2-dimensional Stein manifold with boundary is invariant under self-diffeomorphisms fixing the boundary.
|Autori:||LISCA P; MATIC G|
|Titolo:||Stein 4-manifolds with boundary and contact structures|
|Anno del prodotto:||1998|
|Digital Object Identifier (DOI):||10.1016/S0166-8641(97)00198-3|
|Appare nelle tipologie:||1.1 Articolo in rivista|