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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 17th 2021
   • (edited Jul 17th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added hyperlinks to * [[Franc Forstnerič]], _Oka manifolds_, Comptes Rendus Mathematique, Acad. Sci. Paris 347 (2009), 1017&#8211;20 ([arXiv:0906.2421](https://arxiv.org/abs/0906.2421), [doi:10.1016/j.crma.2009.07.005](https://doi.org/10.1016/j.crma.2009.07.005)) * [[Franc Forstnerič]], _Oka maps_, Comptes Rendus Mathematique, Acad. Sci. Paris, Ser. I 348 (2010) 145-148 ([arxiv/0911.3439](http://arxiv.org/abs/0911.3439), [doi:10.1016/j.crma.2009.12.004](https://doi.org/10.1016/j.crma.2009.12.004)) and added pointer to * [[Franc Forstnerič]], [[Finnur Lárusson]], *Survey of Oka theory*, New York J. Math., 17a (2011), 1-28 ([arXiv:1009.1934](https://arxiv.org/abs/1009.1934), [eudml:232963](https://eudml.org/doc/232963)) * [[Franc Forstnerič]] (appendix by [[Finnur Lárusson]]), *Oka manifolds: From Oka to Stein and back*, Annales de la Faculté des sciences de Toulouse, Mathématiques, Série 6, Tome 22 (2013) no. 4, pp. 747-809 ([numdam:AFST_2013_6_22_4_747_0](https://afst.centre-mersenne.org/item/?id=AFST_2013_6_22_4_747_0)) From the latter I quoted the fact (now [this Prop.](https://ncatlab.org/nlab/show/Oka+manifold#ComplexProjectiveSpaceIsOkaManifold)) that complex projective space is Oka. On another note, I am suspecting that there is little material that wouldn't want to go both to *[[Oka manifold]]* and *[[Oka principle]]* and am thinking the two might need to be merged. <a href="https://ncatlab.org/nlab/revision/diff/Oka+manifold/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/Oka+manifold/5">v5</a>, <a href="https://ncatlab.org/nlab/show/Oka+manifold">current</a>

   I have added hyperlinks to

   • Franc Forstnerič, Oka manifolds, Comptes Rendus Mathematique, Acad. Sci. Paris 347 (2009), 1017–20 (arXiv:0906.2421, doi:10.1016/j.crma.2009.07.005)

   • Franc Forstnerič, Oka maps, Comptes Rendus Mathematique, Acad. Sci. Paris, Ser. I 348 (2010) 145-148 (arxiv/0911.3439, doi:10.1016/j.crma.2009.12.004)

   and added pointer to

   • Franc Forstnerič, Finnur Lárusson, Survey of Oka theory, New York J. Math., 17a (2011), 1-28 (arXiv:1009.1934, eudml:232963)

   • Franc Forstnerič (appendix by Finnur Lárusson), Oka manifolds: From Oka to Stein and back, Annales de la Faculté des sciences de Toulouse, Mathématiques, Série 6, Tome 22 (2013) no. 4, pp. 747-809 (numdam:AFST_2013_6_22_4_747_0)

   From the latter I quoted the fact (now this Prop.) that complex projective space is Oka.

   On another note, I am suspecting that there is little material that wouldn’t want to go both to Oka manifold and Oka principle and am thinking the two might need to be merged.

   diff, v5, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 17th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the statement ([here](https://ncatlab.org/nlab/show/Oka+manifold#CosetSpacesOfComplexLieGroupsAreOkaManifolds)) that coset space of complex Lie groups are Oka manifolds <a href="https://ncatlab.org/nlab/revision/diff/Oka+manifold/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Oka+manifold/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Oka+manifold">current</a>

   added the statement (here) that coset space of complex Lie groups are Oka manifolds

   diff, v6, current

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJul 18th 2021
   • (edited Jul 18th 2021)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThe complement of any compact polynomially convex subset of $\mathbf{C}^n$ ($n\gt1$) is an Oka manifold. (Kusakabe \cite[Theorem 1.2, Corollary 1.3]{Kusakabe}.) <a href="https://ncatlab.org/nlab/revision/diff/Oka+manifold/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/Oka+manifold/8">v8</a>, <a href="https://ncatlab.org/nlab/show/Oka+manifold">current</a>

   The complement of any compact polynomially convex subset of $\mathbf{C}^n$ ($n\gt1$) is an Oka manifold. (Kusakabe \cite[Theorem 1.2, Corollary 1.3]{Kusakabe}.)

   diff, v8, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 19th 2021
   • (edited Jul 19th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. That `\cite`-syntax is not supported here, but a simpler syntax is: I have fixed it to `[Kusakabe 20, Theorem 1.2, Corollary 1.3](#Kusakabe20)` ([here](https://ncatlab.org/nlab/show/Oka+manifold#ComplementsOfCompactPolynomiallyConvextSubsets)). <a href="https://ncatlab.org/nlab/revision/diff/Oka+manifold/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Oka+manifold/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Oka+manifold">current</a>

   Thanks. That \cite-syntax is not supported here, but a simpler syntax is: I have fixed it to [Kusakabe 20, Theorem 1.2, Corollary 1.3](#Kusakabe20) (here).

   diff, v9, current