2021
DOI: 10.4153/s0008414x2100016x
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Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds

Abstract: We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact Hamiltonian torus manifolds to define geometric quantization from the view point of index theory. We give two applications. The first one is a proof of a [Q,R]=0 type theorem, which can be regarded as a proof of the Vergne conjecture for Abelian case. The other is a Danilov-typ… Show more

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