The classical de Rham isomorphism between the singular cohomology

of a smooth manifold $M$ and its de Rham cohomology is a well-known theorem.

In this talk we will consider Riemannian manifolds that admit a certain

triangulation $h: K \to M$, where $K$ is a simplicial complex in $\mathbb{R}^n$.

We will establish the notion of $L_p$-norms for differential forms on $M$

as well as for simplicial cochains on $K$. These define two cochain complexes

$L_p(K)$ and $L_p(M)$. Its cohomologies $H_p(K)$ and $H_p(M)$ are

the $L_p$-cohomology of $M$. We will discuss a variant $H_p(K) \to H_p(M)$

of the de Rham isomorphism that holds in this particular setting. We will

also sketch some other aspects of $L_p$-spaces. A full script is available

at http://math.nikno.de/

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