Rabinowitz Floer homology: A survey
Peter Albers, Urs Frauenfelder
TL;DR
This survey reviews Rabinowitz Floer homology, a Morse homology theory for symplectic and contact topology, highlighting its construction, applications, and relation to Hamiltonian dynamics and magnetic fields.
Contribution
It provides a comprehensive overview of Rabinowitz Floer homology, detailing its construction and diverse applications in symplectic and contact topology.
Findings
Constructed Rabinowitz Floer homology framework.
Applied to symplectic and contact topology problems.
Connected to Hamiltonian perturbations and magnetic fields.
Abstract
Rabinowitz Floer homology is the semi-infinite dimensional Morse homology associated to the Rabinowitz action functional used in the pioneering work of Rabinowitz. Gradient flow lines are solutions of a vortex-like equation. In this survey article we describe the construction of Rabinowitz Floer homology and its applications to symplectic and contact topology, global Hamiltonian perturbations and the study of magnetic fields.
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