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Generic metrics and connections on spin- and \(\text{spin}^c\)-manifolds. (English) Zbl 0899.53036
The present paper gives a detailed investigation of the kernel of the Dirac operator on a \(\text{spin}^c\)-manifold. The author studies the dependence of the dimension of the Dirac operator on the Riemannian metric of the underlying manifold as well as on the connection in the canonical line bundle of a fixed \(\text{spin}^c\)-structure. He also discusses applications to Seiberg-Witten theory.

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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