Differential Geometry and Topology

course: New aspects of the ddc-lemma

speaker: Gil Cavalcanti (University of Oxford)

abstract: The strong Lefschetz property, ddc-lemma and their consequences (such as even odd betti numbers, degeneracy of the Frolicher spectral sequence at E1 and formality) are tools frequently used to tell apart purely symplecticcomplex manifolds from the more special Kaehler manifolds. In generalized complex geometry, an area recently introduced by Hitchin and Gualtieri which incorporates symplectic and complex geometries, one also has a splitting d = del + delbar and the operator dJ = -i(del - delbar) plays an analogous role to that of the complex dc. With that, one can state a "ddJ-lemma". If the generalized complex structure is induced by a complex structure, this lemma is just the standard ddc-lemma, while in the case of a symplectic manifold, it is equivalent to the strong Lefschetz property.

In this talk, I shall introduce generalized complex manifolds and study which implications of the ddc-lemma remain valid.

timetable:
Tue 9 Nov, 10:00 - 11:15, Sala Conferenze Centro De Giorgi
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