Timeline for Analog of Newlander–Nirenberg theorem for real analytic manifolds

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Dec 23, 2018 at 23:49	comment	added	Brian Street		$q$ can be greater than the dimension. It only has to be a spanning set, not a basis. That actually takes a little bit of extra work. Also, this is mostly a local thing, so global topological issues don't come up too much. Because of this, I think it should be possible to turn this into a theorem about some kind of compatible families of vector fields defined locally. But my interests were towards a different sort of question, so I haven't pursued that yet.
Dec 23, 2018 at 23:35	vote	accept	Igor Khavkine
Dec 22, 2018 at 21:38	comment	added	Igor Khavkine		Wow, this is essentially the kind of answer that I was hoping for. Thank you! And these results seem to be coming from your own papers, so I congratulate you on doing very interesting work! A small question. The number of vector fields, $q$, does it have to equal the dimension of the manifold $M$, or could it be larger? For topological reasons, not all manifolds are framed. In these cases, with $q=\dim M$, one could not keep the vector fields globally defined and spanning $TM$. But with a larger number of vector fields, this is of course possible.
Dec 21, 2018 at 17:36	history	answered	Brian Street	CC BY-SA 4.0