Vanishing and Residue of Pontryagin Classes on Singular Foliations
DOI:
https://doi.org/10.54097/qaqcdg95Keywords:
Characteristic classes, singular foliations, manifold topology, higher structures.Abstract
In this paper, we study the vanishing and residue of the Pontryagin classes on singular foliations on smooth manifolds. Specifically, we extend the Bott Vanishing Theorem to singular foliations that admit resolutions by vector bundles, which can be represented by -algebroids, and subsequently prove the Residue Existence Theorem for this type of singular foliations. Our results provide a way of computing the characteristic classes, particularly the Pontryagin classes on smooth manifolds using cohesive modules developed by J. Block. This approach potentially offers a new path in studying the differential geometry and topology of singular foliations beyond the traditional operator algebraic approach.
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