Reduced $L_{q,p}$-Cohomology of Some Twisted Products (La cohomologie $L_{q,p}$ réduite de quelques produits twistés)

摘要

Vanishing results for reduced $L_{q,p}$-cohomology are established in the case of twisted products, which are a generalization of warped products. Only the case $q le p$ is considered. This is an extension of some results by Gol$^{prime }$dshtein, Kuz$^{prime }$minov and Shvedov about the $L_{p}$-cohomology of warped cylinders. One of the main observations is the vanishing of the “middle-dimensional” cohomology for a large class of manifolds.