Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes
In this thesis, we shall study Floer theory for Lagrangian immersions. In the first chapter, we prove a decomposition theorem for pseudo-holomorphic disks with boundary on a given generic Lagrangian immersion. We apply this result to the computation of certain Floer complexes. We conclude with work in progress on the computation of the obstruction of the surgery of two transverse Lagrangian submanifolds. In the second chapter, we consider surfaces. We show that a cobordism group, whose relations are given by unobstructed immersed lagrangian cobordisms, is isomorphic to the Grothendieck group of the derived Fukaya category. We also compute the immersed Lagrangian cobordism group.
Lagrangian submanifolds Lagrangian immersions Holomorphic polygons Lagrangian cobordisms Cobordism groups Floer homology Fukaya categories