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Alp\"oge constructed a complex structure on $S^6$ through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family is Oka and that the family projection over each relatively compact parameter disc is an Oka map. The Oka property survives the deletion or...
Let $\pi:Z\rightarrow Y$ be a smooth projective morphism of complex manifolds with connected rationally connected fibers. We prove holomorphic approximation on arbitrary compact sets and finite-jet interpolation on arbitrary closed discrete sets for continuous liftings defined on open Riemann surfaces and holomorphic n...
The homotopy types of Oka manifolds are exactly those of countable finite-dimensional CW complexes. We construct realizations as open subsets of complex Euclidean spaces with explicit dimension bounds. Other realizations have good open covers by sets biholomorphic to $\C^N$, with prescribed finite nerves, or are unions...
We introduce the local approximation propert (LAP) and prove that it characterizes Oka manifolds. We prove that LAP yields convex approximation and, in an $n$-dimensional target, propagates across sets of zero $(2n-1)$-dimensional Hausdorff measure. Consequently, strong dominability characterizes Oka manifolds, convex...
We prove that a holomorphic family of connected complex Lie groups has Oka total space if and only if its base is Oka. Extension presentations and generating sections give Oka results for stable and parabolic bundle moduli and for holomorphic mapping and embedding spaces. Every nonempty degree component of maps from a...
Starting from Alp\"oge's torus fibration with exactly three special fibres on a complex six-sphere, we construct a locally miniversal family of compact complex threefolds. Every member is Oka, and the projection over each relatively compact parameter disc is an Oka map. Deleting or simultaneously blowing up finitely ma...
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