Oka complements of countable sets and non-elliptic Oka manifolds

Abstract

We study the Oka properties of complements of closed countable sets in ${\mathbb{C}}^n(n>1)$ which are not necessarily discrete. Our main result states that every tame closed countable set in ${\mathbb{C}}^n(n>1)$ with a discrete derived set has an Oka complement. As an application, we obtain non-elliptic Oka manifolds which negatively answer a long-standing question of Gromov. Moreover, we show that these examples are not even weakly subelliptic. It is also proved that every finite set in a Hopf manifold has an Oka complement and an Oka blowup.

7 pages

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