The hexagon from a fracture square

https://zoom.us/j/99428054844?pwd=NXlRVmJobUhFZTFtQUQrZ29RZk81dz09

Meeting-ID: 994 2805 4844
For passcode contact Christian Kaiser (kaiser@mpim...).

Differential cohomology groups are not necessarily homotopy invariant refinements of cohomology theories on smooth manifolds. In previous talks, we introduced one variant (Deligne cohomology) and explained how the higher-categorical notion of  a sheaf of spectra on the site of manifolds gives rise to a differential cohomology theory. This week we give a systematic treatment of breaking up the category of such sheaves, an individual sheaf, and morphisms between two sheaves via the notion of a recollement of stable ∞-categories. We explain how this gives rise to the hexagon that was the central player in the axiomatic treatment of differential cohomology by Sullivan and Simon, allows one to study possible differential refinements of a given cohomology theory, and show that the Chern-Weil construction of characteristic classes has a unique lift to Deligne cohomology.