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The research activities of this unit are devoted to various aspects of differential geometry : symplectic geometry, Kähler geometry, deformation quantization, symplectic and contact topology.
Multi-dimensional Morse theory
The central object is a map between manifolds. We consider the topological complexity both of the image and of the level sets of such maps as it can be measured by topological invariants such as the rank of the (co)homology, the minimal number of cells in a cell decomposition, the minimal number of generators of the fundamental group or the minimal number of critical points of a Morse function.
Topological symplectic manifolds
Study and comparison of different definitions of topological symplectic manifolds. Tentative constructions of examples.