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Zero sets of eigenspinors for generic metrics
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classification
math.DG
keywords
diraceigenspinorsfixedgenericoperatorspinzeroclosed
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abstract
Let $M$ be a closed connected spin manifold of dimension $2$ or $3$ with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on $M$ the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.
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