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Oka complements of countable sets and nonelliptic Oka manifolds
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We study the Oka properties of complements of closed countable sets in
C
n
(
n
>
1
)
\mathbb {C}^{n}\ (n>1)
which are not necessarily discrete. Our main result states that every tame closed countable set in
C
n
(
n
>
1
)
\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.
American Mathematical Society (AMS)
Title: Oka complements of countable sets and nonelliptic Oka manifolds
Description:
We study the Oka properties of complements of closed countable sets in
C
n
(
n
>
1
)
\mathbb {C}^{n}\ (n>1)
which are not necessarily discrete.
Our main result states that every tame closed countable set in
C
n
(
n
>
1
)
\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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