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Results tagged with derham-cohomology
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user 402
Better spelling "DeRham", not derham... I can't figure out how to change this... moderators? The cohomology of the complex of differential forms on a smooth manifold with differential given by exterior derivative.
14
votes
Accepted
De Rham via topoi
One can define an analogue of the crystalline topos for smooth manifolds.
This is known as the de Rham stack of $M$.
One of the easiest constructions of the de Rham stack
embeds smooth manifolds fully …
- 37.8k
11
votes
Can one glue De Rham cohomology classes on a differential manifolds?
This answer provides a positive answer to a refinement of the original question.
Recall that two closed differential $k$-forms $ω_0$, $ω_1$ on a smooth manifold $M$
have the same de Rham cohomology cl …
- 37.8k
10
votes
Direct proof that Chern-Weil theory yields integral classes
Yes, the Chern–Weil homomorphism lifts to differential cohomology,
which guarantees that periods are integral.
See the original paper by Cheeger and Simons, or the paper by Hopkins and Singer.
The (mo …
- 37.8k
4
votes
Can one make sense of de Rham cohomology for the complement of a (dense) irrational flow on ...
Any foliation gives rise to two Lie groupoids (monodromy and foliation, see for example the book of Moerdijk–Mrčun),
and a Lie groupoid gives rise to a simplicial presheaf on the site of smooth manifo …
- 37.8k