Abstract
We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of a family of transversal Dirac operators relative to a Riemannian foliation. The family in question is parameterized by a moduli space of basic connections with respect to the foliation modulo a suitable group of foliation preserving gauge transformations. The proof is based on the concept of spectral flow, applied to the suspension of suitable gauge transformations to periodic families of Dirac operators.
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Work supported in part by a grant from the National Science Foundation.
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Glazebrook, J.F., Kamber, F.W. On spectral flow of transversal dirac operators and a theorem of Vafa-Witten. Ann Glob Anal Geom 9, 27–35 (1991). https://doi.org/10.1007/BF02411353
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DOI: https://doi.org/10.1007/BF02411353