Morse–Floer theory for superquadratic Dirac equations, II: construction and computation of Morse–Floer homology

We give a construction and computation of Morse–Floer homology for a class of superquadratic Dirac functionals defined on the set of spinors on a compact spin manifold. For the superquadratic functionals, we show that the Morse–Floer homology is well defined for generic choice of metric on the set of spinors and its isomorphism class is independent of the choice of such a generic metric. Moreover, we show that it is also independent of the choice of superquadratic Dirac functional. Therefore, it defines an invariant for the set of spinors which we call the superquadratic-Dirac–Morse–Floer homology. We prove a vanishing result for this homology. As an application, we give existence and multiplicity results for a class of superquadratic Dirac equations on compact spin manifolds.