Rabinowitz Floer homology (A06)

• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

Rabinowitz Floer homology (RFH) is a powerful algebraic invariant of contact-type compact hypersurfaces inside symplectic manifolds. The aim of this project is to develop RFH further, with an eye towards applications. In particular, we intend to study relations of RFH to other Floer homologies, product structures on RFH, equivariant versions and the behaviour of RFH under surgery constructions. We expect to derive applications about multiplicity and linear stability of periodic orbits of Reeb flows and translated points of contactomorphisms, orderablity of contact manifolds, lower bounds on the complexity of Reeb flows and positive contactomorphisms.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Universität Münster ; Fachbereich 10 - Mathematik und Informatik; Mathematisches Institut; Ruhr-Universität Bochum
• Project Heads: Professor Dr. Alberto Abbondandolo; Professor Dr. Peter Albers