Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations I

Foliations have a theory of characteristic classes that is much like that of vector bundles, but with notable differences. Some of the characteristic classes of a foliation come from its induced normal bundle, but there are additional secondary classes that depend on more detailed information about the foliation. Just as with vector bundles, one can obtain the characteristic classes using either a universal space or the Chern-Weil construction (in case the foliation is regular).

In these talks I will explain the general theory, and how the Chern-Weil construction can often be made to work even for singular foliations.