COLLOQUIUM
3:00 p.m., Friday (November 14, 2008)
MATX 1100
Laurent Meersseman
PIMS/University of Bourgogne
Foliations by Complex Leaves
Abstract: (Codimensionone) foliations by complex leaves are, roughly speaking, smooth partitions of a smooth manifold into complex manifolds of codimensionone (think of \Bbb C^n\times \Bbb R foliated by the level sets of the projection map onto \Bbb R). They are mixed objects, tangentially holomorphic and transversally smooth.
They appear in different situations. Examples include differentiable families of deformations of compact complex manifolds, Leviflat hypersurfaces in complex projective space, every oriented 2dimensional smooth foliation. But there exist also more exotic ones as a foliation of the 5sphere by complex surfaces.
They can be seen as generalized deformations of complex manifolds, or as generalized complex structures on odddimensional smooth manifolds.
In this talk, I will explain the notion of foliations by complex leaves and describe (some of) the previous examples in detail. Then, taking the viewpoint of generalized deformations, I will compare classical deformations and foliated deformations in the particular example of Hopf manifolds.
This is a joint work with M. Nicolau and A. Verjovsky.
Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).
