Geometry and dynamics via contact topology (GEODYCON)
Geometry and dynamics via contact topology
Start date: Jan 1, 2012,
End date: Dec 31, 2016
"I intend to cross ressources of holomorphic curves techniques and traditional topological methods to study some fundamental questions in symplectic and contact geometry such as:- The Weinstein conjecture in dimension greater than 3.- The construction of new invariants for both smooth manifolds and Legendrian/contact manifolds, in particular, try to define an analogue of Heegaard Floer homology in dimension larger than 3.- The link, in dimension 3, between the geometry of the ambient manifold (especially hyperbolicity) and the dynamical/topological properties of its Reeb vector fields and contact structures.- The topological characterization of odd-dimensional manifolds admitting a contact structure.A crucial ingredient of my program is to understand the key role played by open book decompositions in dimensions larger than three.This program requires a huge amount of mathematical knowledges. My idea is to organize a team around Ghiggini, Laudenbach, Rollin, Sandon and myself, augmented by two post-docs and one PhD student funded by the project. This will give us the critical size to organize a very active working seminar and to have a worldwide attractivity and recognition.I also plan to invite one confirmed researcher every year (for 1-2 months), to organize one conference and one summer school, as well as several focused weeks."
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