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.
In Bott and Tu (Differential forms in algebraic topology) there are proofs that both de Rham cohomology and singular cohomology agree with Čech cohomology (with respect to a good cover). In Hatcher (Algebraic topology) you can find a proof that singular and simplical cohomology agree.
Note that the first half of the above (the isomorphism between de Rham and singular cohomology) is often called de Rham's theorem.