Distortion of Mappings and $L_{q,p}$-Cohomology

TL;DR

This paper explores how certain classes of diffeomorphisms influence the $L_{q,p}$-cohomology of manifolds, providing new insights into when this cohomology vanishes or persists.

Contribution

It establishes relationships between geometric diffeomorphisms and $L_{q,p}$-cohomology, offering new applications for vanishing and non-vanishing results.

Findings

Identifies conditions under which $L_{q,p}$-cohomology vanishes.

Provides criteria for non-vanishing of $L_{q,p}$-cohomology.

Links geometric transformations to cohomological properties.

Abstract

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are given.