I'm looking for a recomendable reference/source for a rigorous proof that for manifolds (with "nice enough" structure) the simlicial and De Rham (co)homologies coincide.

Especially, I know that there exist criterions from axiomatic (co)homology theories which provide a statement about different (co)homology theories just if the neccessary conditions are fullfilled.

But I'm looking preferably for a reference where a concrete isomorphism between both (co)homologies above is constructed. So with viewpoint to geometric intuition.

  • $\begingroup$ I do not know for DeRahm homology, but you can see on "Lectures on algebraic topology" from Matveev, there is a section (1.11) that presents an axiomatic approach that guaranty that all homology verifying those axioms are isomorphic. $\endgroup$ – Paul Cottalorda Feb 4 at 16:10
  • $\begingroup$ I think your problem might be that there are smooth manifolds without a simplicial structure. $\endgroup$ – Randall Feb 4 at 16:12
  • $\begingroup$ @Randall: this reflects my vague formulation "...with "nice enough" structure...". So we can for example assume that considered manifolds have simplicial structure $\endgroup$ – KarlPeter Feb 4 at 16:34
  • $\begingroup$ My guess is that would be tough, because you need those "nice enough" structures to be stable enough for excision, M-V, etc. $\endgroup$ – Randall Feb 4 at 18:45

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