Morse–Floer theory for superquadratic Dirac equations, II: construction and computation of Morse–Floer homology
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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.
KeywordsSuperquadratic Dirac equations Morse–Floer homology
Mathematics Subject Classification35Q41 37B30 57R58 58E05
The author wishes to express his sincere gratitude to Dr. A. Maalaoui for interesting discussions related to this paper. The author also would like to express his appreciation to anonymous referee for his/her careful reading of the manuscript and helpful suggestions. This work was supported by JSPS KAKENHI Grant Numbers 22540222, 15K04947.
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