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

Vladimir Gol'dshtein; Yaroslav Kopylov

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arXiv · 1505.00913

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

Vladimir Gol'dshtein·Yaroslav Kopylov

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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 $q \leq p$ 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".

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Vladimir Gol'dshtein, Yaroslav Kopylov. 2015-05-05. Reduced $L_{q,p}$-Cohomology of Some Twisted Products. https://arxiv.org/abs/1505.00913

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