symp-foliations

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start [2017/07/26 15:21]
alvaro 		start [2017/08/29 17:14] (Version actuelle)
alvaro [Symplectic foliations]
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 ====== Symplectic foliations ====== ====== Symplectic foliations ======
  
-The purpose of the workshop is to explore whether one may be able to define interesting classes of foliations in higher dimensions by taking a symplectic viewpoint. We say that a foliation is [symplectic[symplectic]] if it admits a leafwise symplectic form. If this form arises from a global closed 2-form we say that the foliation is  [[strong symplectic |strong]] or 2-calibrated. Certain symplectic techniques only extend (naively) to the strong setting: Donaldson techniques and cohomological energy estimates for pseudoholomorphic curves do require closeness.+The purpose of the workshop is to explore whether one may be able to define interesting classes of foliations in higher dimensions by taking a symplectic viewpoint. We say that a foliation is [[symplectic |symplectic]] if it admits a leafwise symplectic form. If this form arises from a global closed 2-form we say that the foliation is  [[strong symplectic |strong]] or 2-calibrated. Certain symplectic techniques only extend (naively) to the strong setting: Donaldson techniques and cohomological energy estimates for pseudoholomorphic curves do require closeness.
  
 The following is a tentative list of potentially interesting topics for the workshop: The following is a tentative list of potentially interesting topics for the workshop:
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   * [[Obstructions to existence of symplectic foliations|Obstructions to existence]]. In the opposite direction, there are no known obstructions to the existence of strong symplectic foliations (apart from the obvious formal ones). Does a Novikov type theorem hold in this setting? What are some reasonable hypothesis for such a statement?   * [[Obstructions to existence of symplectic foliations|Obstructions to existence]]. In the opposite direction, there are no known obstructions to the existence of strong symplectic foliations (apart from the obvious formal ones). Does a Novikov type theorem hold in this setting? What are some reasonable hypothesis for such a statement?
  
-  * The [[Confoliations|confoliation programme]]. The formal data underlying a symplectic foliation and a contact structure is the same. Is it possible to reproduce Eliashberg and Thurston’s confoliation result in higher dimensions? Is it perhaps simpler to carry it out if one assumes strongness?+  * [[The confoliation programme|The confoliation programme]]. The formal data underlying a symplectic foliation and a contact structure is the same. Is it possible to reproduce Eliashberg and Thurston’s confoliation result in higher dimensions? Is it perhaps simpler to carry it out if one assumes strongness?
  
   * [[Pseudoholomorphic curve theory]]. In the strong case, under reasonable assumptions, moduli spaces of pseudoholomorphic curves should be compact manifolds endowed with singular foliations where the leaves correspond to the leafwise moduli spaces. What structure results for strong symplectic foliations can be obtained this way? What about classification results for fillings of contact foliations?   * [[Pseudoholomorphic curve theory]]. In the strong case, under reasonable assumptions, moduli spaces of pseudoholomorphic curves should be compact manifolds endowed with singular foliations where the leaves correspond to the leafwise moduli spaces. What structure results for strong symplectic foliations can be obtained this way? What about classification results for fillings of contact foliations?
Ligne 52: Ligne 52:
  
   *    Transverse Hamiltonian dynamics. Strong symplectic foliations are not stable Hamiltonian usually, but there is a well defined notion of Reeb vector field. What can be said about its dynamics?   *    Transverse Hamiltonian dynamics. Strong symplectic foliations are not stable Hamiltonian usually, but there is a well defined notion of Reeb vector field. What can be said about its dynamics?
 +
 +
 +====== Research ideas/questions =====
 +
 +The following is a list of the particular topics and questions brought up by the participants.
 +
 +  *  [[Differential operators and foliations]]
 +
 +  *  [[Transverse submanifolds and foliations]]
 +
 +  *  [[Existence of symplectic foliations]]
 +
 +  *  [[The confoliation programme]]
 +
 +  *  [[Deformations of symplectic foliations]]
 +
 +  *  [[Foliated symplectic topology]]
 +
  
start.1501075309.txt.gz · Dernière modification: 2017/07/26 15:21 de alvaro

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