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

Vladimir Gol’dshtein | Zendy; Yaroslav Kopylov | Zendy

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

Author(s) -

Vladimir Gol’dshtein,

Yaroslav Kopylov

Publication year - 2016

Publication title -

annales mathématiques blaise pascal

Language(s) - English

Resource type - Journals

eISSN - 2118-7436

pISSN - 1259-1734

DOI - 10.5802/ambp.359

Subject(s) - cohomology , mathematics , generalization , pure mathematics , extension (predicate logic) , čech cohomology , class (philosophy) , de rham cohomology , equivariant cohomology , mathematical analysis , computer science , artificial intelligence , programming language

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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