De Rham's theorem for Orlicz cohomology

TL;DR

This paper establishes an isomorphism between de Rham $L^$-cohomology and simplicial $$-cohomology for Riemannian manifolds with triangulations, demonstrating invariance under quasi-isometries.

Contribution

It proves the isomorphism between de Rham $L^$-cohomology and simplicial $$-cohomology for manifolds with triangulations, extending the understanding of Orlicz cohomology.

Findings

Isomorphism between de Rham and simplicial cohomology in Orlicz spaces

Quasi-isometry invariance of de Rham $L^$-cohomology

Applicability to manifolds admitting a convenient triangulation

Abstract

We prove that the de Rham $L^\phi$-cohomology of a Riemannian manifold $M$ admiting a convenient triangulation $X$ is isomorphic to the simplicial $\ell^\phi$-cohomology of $X$ for any Young function $\phi$. This result implies the quasi-isometry invariance of the first one.