Homology on manifolds

The additional structure of coordinates and tangents can be used to revisit homology, gaining additional insight and results. In particular, as we saw in the previous section, the exterior derivative \({\mathrm{d}}\) exhibits structure reminiscent of the boundary homomorphism \({\partial}\) in homology. This can be exploited to build a version of homology based on forms instead of on simplices.

An Illustrated Handbook