| analytic integration | cohomological integration |
|---|---|
| measure | orientation in generalized cohomology |
| Riemann/Lebesgue integration, of differential forms | push-forward in generalized cohomology/in differential cohomology |
integration over supermanifolds, Berezin integral, fermionic path integral
Kontsevich integral, Selberg integral, elliptic Selberg integral
The refinement of the notion of fiber integration in generalized (Eilenberg-Steenrod) cohomology to differential cohomology.
Section 4.10 in