Fortführung und Erweiterung des Projektes `Functoriality for Floer homology` und Erlernen der neuen Techniken entwickelt von H. Hofer

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The object of the proposed project is the theory of Floer homology in symplectic geometry. The principal problem to be analyzed is the question of functoriality for Floer homology with respect to symplectic immersions of positive codimension. This will lead to a large number of important new applications concerning e.g. symplectic invariants such as capacities and Gromov-Witten invariants and Lagrangian intersection results. We are using an approach based on a Lagrangian boundary value problem for Floer half-cylinders. The main problems are to extend this concept in broad generality which requires a careful analysis of holomorphic disks and to develop a suitable concept of obstruction classes and algebraic correction terms. We expect the new techniques currently developed by H. Hofer to be crucial in pursuing this project.