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Koszul complexes, Birkhoff normal form and the magnetic Dirac operator (1511.08545v1)
Published 27 Nov 2015 in math.AP, math.DG, and math.SP
Abstract: We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuations combined with the Birkhoff normal form and local index theory.
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