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Aug 24, 2017 at 19:15 vote accept user56980
Jun 13, 2017 at 6:09 comment added Sebastian Goette @მამუკაჯიბლაძე You get a secondary class for variations of metrics, and from degree 3 on, there are variational classes to compare two flat connections joined by a path of flat connections. I am not aware of any classes for non-flat connections, except the original Chern-Weil forms from which the Kamber-Tondeur or Bismut-Lott classes were derived.
Jun 12, 2017 at 6:55 comment added მამუკა ჯიბლაძე Very interesting. Does this then produce some version of secondary chern-cheeger-simons-whoever classes for non-flat connections??
Jun 12, 2017 at 6:40 history answered Sebastian Goette CC BY-SA 3.0