Abstract
We study necessary and sufficient conditions for an approximately differentiable map between Riemannian manifolds to induce a bounded transfer operator of differential forms with respect to the norms of Lebesgue spaces. As a corollary, we see that every homeomorphism of class whose transfer operator of differential forms with norm in is an isomorphism must necessarily be either quasi-conformal or quasi-isometric. We give some applications of our results to the study of the functoriality of cohomology in Lebesgue spaces.
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