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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Added an example (dR cohomology for spheres) with a very sketchy proof sketch. More examples, worked out in more detail, to follow. Might make a de Rham cohomology page and move the examples there.
Mark Moon
added statement of the relation to the PL de Rham complex (here)
Added:
Explicitly, given a differential $k$-form $\omega$, its de Rham differential $d\omega$ can be computed as
$d\omega(v_0,\ldots,v_k)=\sum_i (-1)^i \mathcal{L}_{v_i} \omega(v_0,\ldots,v_{i-1},v_{i+1},\ldots,v_k)+\sum_{i<j}(-1)^{i+j}\omega([v_i,v_j],v_0,\ldots,v_{i-1},v_{i+1},\ldots,v_{j-1},v_{j+1},\ldots,v_k),$where $v_i$ are vector fields on $X$, $[-,-]$ is the Lie bracket of vector fields, and $L_{-}$ is the Lie derivative of a smooth function with respect to a vector field.
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