Titlebook: Stein Manifolds and Holomorphic Mappings; The Homotopy Princip Franc Forstnerič Book 2017Latest edition Springer International Publishing A

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Elliptic Complex Geometry and Oka Theoryof holomorphic sections over small open sets in the base .. We give a relative Oka principle for sections of certain branched holomorphic maps, and we prove a Runge type approximation theorem for algebraic maps from affine algebraic varieties to a certain class of algebraic manifolds.

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Embeddings, Immersions and Submersionsn spaces, the homotopy principle for holomorphic submersions from Stein manifolds, and the construction of nonsingular holomorphic foliations on Stein manifolds. An important technical result proved in this chapter is a splitting lemma for biholomorphic maps close to the identity on a Cartan pair.

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Preliminariesphic fibre bundles and especially vector bundles, the tangent and cotangent bundle of a complex manifold, differential forms, de Rham and Dolbeault cohomology, plurisubharmonic functions, the Levi form, vector fields and their flows. We also recall a basic form of Gromov’s homotopy principle for fir

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Stein Manifolds-Thullen characterization of domains of holomorphy by holomorphic convexity, the notions of Hartogs and Levi pseudoconvexity, the Levi problem, the basic characterizations of Stein manifolds and Stein spaces, Cartan-Serre Theorems A and B and their immediate applications, holomorphic embedding theor

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Automorphisms of Complex Euclidean Spaces. The main focus is the Andersén-Lempert theory and its generalization to complex manifolds enjoying Varolin’s density property. This subject is closely intertwined with Oka theory and furnishes important examples of Oka manifolds. Our knowledge of the class of Stein manifolds with the density prope

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Oka Manifoldsogical classification of principal fibre bundles over Stein spaces agrees with the holomorphic classification. Next we describe a reduction to the problem of deforming families of continuous sections to families of holomorphic sections in principal fibre bundles over Stein spaces. This naturally lea

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Elliptic Complex Geometry and Oka Theoryduced Stein space .. The main result is a theorem of Gromov from 1989 and several of its generalizations. Roughly stated, it says that the existence of a finite dominating family of holomorphic fibre sprays on . over each sufficiently small open subset of . (a submersion with this property is said t

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