2022/10/25 by Maxim Braverman, Braverman, Maxim, Ahmad Reza Haj Saeedi Sadegh +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2210.14359
In this paper, we construct a smooth vector bundle over the deformation to the normal cone DNC(V,M) through a rescaling of a vector bundle E→ 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.