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Seminários do IMPA

Geometria Diferencial

A symplectic generalization of 3-dimensional taut foliations
David Martínez Torres

Terça-feira, 23 de abril de 2019, 15:30
Sala 236.

A taut foliation on a closed 3-manifold is a foliation by surfaces which has a transverse cycle meeting every leaf. Equivalently, it has a closed 2-form which induces an area form on each leaf. 

In arbitrary dimensions, and from a symplectic view point, it makes sense to look at codimension  one foliations with a closed 2-form making each leaf symplectic. We shall recall how Donaldson approximately holomorphic theory for symplectic manifolds can be adapted to this class of foliations, to produce "Donalson divisors'' which generalize the transverse cycles in the 3-dimensional case. Finally, we shall discuss a foliated version of the Lefschetz hyperplane theorem which implies that Donaldson divisors capture entirely the transverse geometry of the ambient foliation.