Oka complements of countable sets and nonelliptic Oka manifolds

Kusakabe, Yuta

doi:10.1090/proc/14832

Oka complements of countable sets and nonelliptic Oka manifolds
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Proc. Amer. Math. Soc. 148 (2020), 1233-1238 Request permission

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 nonelliptic 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.

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