Construction of Constrained Floer Homology

We consider the symplectic area functional, constrained to loops of vanishing Hamiltonian mean value: It has the same critical points as the Rabinowitz action functional, and can be used to define a similar Floer homology. In contrast to RFH, it admits an intrinsic product structure, but also involves a non-local term in the gradient flow equation.

This talk will delve into the Fredholm and compactness results required to define CFH, and also discuss some remaining „mysteries“.