Recent developments on Oka manifolds
Franc Forstnerič
Abstract
In this paper we present the main developments in Oka theory since the publication of my book Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis), Second Edition, Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for n>1 the fibre ℂn in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.
Topics & Concepts
MathematicsHomotopyPure mathematicsEuclidean geometryHolomorphic functionDegenerate energy levelsStein manifoldFiber bundleAlgebra over a fieldProjective testGeometryFiberComplex manifoldOrganic chemistryPhysicsChemistryQuantum mechanicsHolomorphic and Operator TheoryGeometric and Algebraic TopologyGeometric Analysis and Curvature Flows