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— transverse_submanifolds_and_foliations [2017/08/29 17:01] (Version actuelle)
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 +===== Transverse submanifolds and foliations =====
 +
 +  * **(Ioan Marcut)** Strong symplectic foliations of codimension-1 admit strong symplectic divisors as a consequence of Donaldson theory. What about foliations of higher codimension? (It is worth pointing out that in codimension-1 one obtains a non-singular foliation because of the symplectic analogue of Bertini's theorem: singular divisors generically appear in real families of dimension at least 2.) What about weak symplectic foliations, to which Donaldson theory does not apply?
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 +  * **(M. Bertelson)** The kernel of a closed 2-form of constant rank is a transversally symplectic foliation. Is there a notion of duality between tangentially symplectic foliations and transversally symplectic foliations? In particular, given a transversally symplectic foliation, can one find a foliation transverse to it (which is then strong symplectic)? It is not even known whether an h-principle holds for transversally symplectic foliations on open manifolds. There is some progress regarding Seiberg-Witten for transversally symplectic foliations due to Kordyukov, Lejmi and Weber.
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 +  * **(Y. Mitsumatsu)** This relates to the previous question: what can be said about symplectic manifold foliated by symplectic submanifolds?
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 +  * **(Y. Mitsumatsu)** What about relations with other classes of foliations with tangent/transverse structure? What about the relation between transversely contact foliations with Engel structures?
  
transverse_submanifolds_and_foliations.txt · Dernière modification: 2017/08/29 17:01 de alvaro

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