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differential_operators_and_foliations
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differential_operators_and_foliations [2017/08/29 16:59] alvaro créée |
differential_operators_and_foliations [2017/08/29 17:11] (Version actuelle) alvaro |
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| + | ===== Differential operators and foliations ===== | ||
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| * **(V. Ginzburg)** Given a (possibly very degenerate) function on a foliated manifold, what is a sufficient condition for a leaf to have a critical point? | * **(V. Ginzburg)** Given a (possibly very degenerate) function on a foliated manifold, what is a sufficient condition for a leaf to have a critical point? | ||
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| * **(M. Bertelson, R. Klaasse)** Is there a foliated version of Seiberg-Witten theory providing obstructions to the existence of a leafwise symplectic structure for foliations of rank 4? | * **(M. Bertelson, R. Klaasse)** Is there a foliated version of Seiberg-Witten theory providing obstructions to the existence of a leafwise symplectic structure for foliations of rank 4? | ||
| - | | + | * Given a foliation by surfaces on a 3-dimensional manifold, is there a way of obtaining 3-dimensional Seiberg-Witten by combining the vortex equation along the leaves coupled with some transverse differential condition? For mapping tori this is sketched by Salamon (1999). Assuming this is true, can this be used to say something about the foliations the 3-manifold admits? Can a similar scheme be used in higher dimensions to cook up invariants as suggested in the previous question? |
differential_operators_and_foliations.1504018750.txt.gz · Dernière modification: 2017/08/29 16:59 de alvaro
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