Fredholm theory and transversality for the parametrized and for the $S_1$-invariant symplectic action
Fredholm theory and transversality for the parametrized and for the $S_1$-invariant symplectic action
We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the _L_2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic _S_1-invariant families of Hamiltonians …