Geometric Dynamic Days 2019

Rabinowitz Floer Homology

RWTH Aachen 2019, 15-16 November

Prof. Dr. Kai Cieliebak
Prof. Dr. Urs Frauenfelder

Abstract. Rabinowitz Floer homology is the semi-infinite dimensional Morse homology in the sense of Floer associated to a Lagrange multiplier action functional used by Rabinowitz in his pioneering work on applying global methods to Hamiltonian dynamics. This action functional detects periodic orbits of fixed energy but arbitrary period. Since the period is allowed to be negative as well one can think of Rabinowitz Floer homology as a kind of Tate version of Symplectic homology. Rabinowitz Floer homology has a broad range of applications to various fields, including the theory of contact embeddings, magnetic fields and Mañé's critical values, translated points, the global perturbation theory of Hamiltonian systems, the contactomorphism group, symplectic homology, and string topology. While the critical point equation is local the gradient flow equation is not local anymore so that one can think of Rabinowitz Floer homology as an example of a nonlocal Floer homology.
In the talks we plan to explain the construction of Rabinowitz Floer homology and discuss some of its applications.

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