Deformation spaces, rescaled bundles, and their applications in geometry and analysis

Abstract: We construct an algebraic vector bundle over the deformation to the normal cone for an embedding of manifolds through a rescaling of a vector bundle over the ambient space. This method generalizes the construction of the spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin Yi. Applications of this construction include local index formula, equivariant index formula, Kirillov formula and Witten and Novikov deformation of de Rham operator.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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