Oka complements of countable sets and nonelliptic Oka manifolds
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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.References
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Additional Information
- Yuta Kusakabe
- Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
- Email: y-kusakabe@cr.math.sci.osaka-u.ac.jp
- Received by editor(s): July 28, 2019
- Published electronically: November 6, 2019
- Additional Notes: This work was supported by JSPS KAKENHI Grant Number JP18J20418.
- Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1233-1238
- MSC (2010): Primary 32E10, 32E30, 32H02; Secondary 32M17
- DOI: https://doi.org/10.1090/proc/14832
- MathSciNet review: 4055950