Reduced $L_{q,p}$-Cohomology of Some Twisted Products

Abstract

Vanishing results for reduced $L_{p,q}$-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'dshtein, Kuz'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. This means that the $L_2$-Betty numbers are zero in the "middle dimension".

arXiv comment15 pages