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Deformation Spaces, Rescaled Bundles and the Kirillov Character Formula

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arxiv 2210.14359 v2 pith:NWJSRNUE submitted 2022-10-25 math.DG

classification math.DG
keywords bundledeformationequivariantapplicationcharacterconeconstructionformula
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abstract

In this paper, we construct a smooth vector bundle over the deformation to the normal cone $\text{DNC}(V,M)$ through a rescaling of a vector bundle $E\to V$, which generalizes the construction of the spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin Yi. We also provide an equivariant version of their construction. As the main application, we recover the Kirillov character formula for the equivariant index of Dirac-type operators. As another application, we get an equivariant generalization of the description of the Witten and the Novikov deformations of the de Rham-Dirac operator using the deformation to the normal cone obtained recently by O. Mohsen.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On Multiplicative Weightings for Lie Groupoids and Lie Algebroids

    math.DG 2025-08 unverdicted novelty 7.0 of 10

    The submission pairs a differential-geometry abstract on Lie groupoid weightings with an unrelated astrophysics manuscript, leaving the claimed results unsupported by the provided text.

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