Mathematisches Kolloquium

Zusammenfassung: The Arnold-Givental conjecture asks for a lower bound in terms of topological datas on the number of intersection points of two Hamiltonian isotopic Lagrangian submanifolds which are fixed point sets of an antisymplectic involution and intersect transversally. Up to now only partial results are proved. Basically all of these approaches are based on Floer homology which interprets the Arnold-Givental conjecture as the Morse inequalities of an action functional. The boundary operator in Floer homology is defined by counting open strings which arise as gradient flow lines of the action functional. The difficulty is, that the moduli spaces of open strings are often non compact, due to the bubbling phenomenon. In order to explain my own contribution to the Arnold-Givental conjecture I will present a particular Lagrange multiplier action functional whose corresponding moduli spaces of open strings have better compactness properties. I will explain how the Lagrange multiplier can be interpreted as curvature of a connection and how gauge theoretic tools lead to the necessary compactness of the moduli spaces.

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