Chern-Weil theory for singular foliations
Year: 2021
Type: preprint
Abstract: We give a Chern-Weil map for the Gel'fand-Fuks characteristic classes of singular Haefliger foliations admitting a large class of singularities. Our characteristic map gives de Rham cohomology representatives for these characteristic classes in terms of a singular Riemannian metric on the manifold that is adapted to singularities. As an application, we give an explicit generalisation to the singular setting of the classical construction of de Rham representatives for the Godbillon-Vey invariant.
Source: arXiv (Cornell University)
Authors: Lachlan MacDonald, Benjamin McMillan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3175256392