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

Golʼdshtein, Vladimir; Kopylov, Yaroslav

doi:10.5802/ambp.359

Reduced

L_{q, p}

-Cohomology of Some Twisted Products
[La cohomologie

L_{q, p}

réduite de quelques produits twistés]

Golʼdshtein, Vladimir ¹ ; Kopylov, Yaroslav ^2,³

¹ Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Beer Sheva 84105, Israel
² Sobolev Institute of Mathematics Pr. Akad. Koptyuga 4 630090, Novosibirsk, Russia
³ Novosibirsk State University ul. Pirogova 2 630090, Novosibirsk, Russia

Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 151-169.

Résumé
Abstract

On établit des résultats d’annulation de la cohomologie $L_{q, p}$ réduite pour les produits twistés, une généralisation des produits tordus dans le cas de $q \leq p$ . Le résultats obtenus sont des généralisations de certains résultats par Gol $^{'}$ dshtein, Kuz $^{'}$ minov et Shvedov sur la cohomologie $L_{p}$ des cylindres tordus. Une des observations principales est la trivialité de la cohomolgie en dimension “moyenne” pour une large classe de variétés.

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 $q \leq p$ 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.

DOI : 10.5802/ambp.359

Classification : 58A10, 58A12
Keywords: differential form, reduced

L_{q, p}

-cohomology, twisted cylinder
Mot clés : forme différentielle, cohomologie

L_{q, p}

réduite, cylindre twisté

Affiliations des auteurs :

Golʼdshtein, Vladimir ¹ ; Kopylov, Yaroslav ^{2, 3}

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     title = {Reduced $L_{q,p}${-Cohomology} of {Some} {Twisted} {Products}},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {151--169},
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Golʼdshtein, Vladimir; Kopylov, Yaroslav. Reduced $L_{q,p}$-Cohomology of Some Twisted Products. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 151-169. doi : 10.5802/ambp.359. https://www.numdam.org/articles/10.5802/ambp.359/

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