Annales Mathématiques
Blaise Pascal
no. 2
Reduced L q,p -Cohomology of Some Twisted Products
[La cohomologie L q,p réduite de quelques produits twistés]
Vladimir Golʼdshtein1 ; Yaroslav Kopylov2, 3
1 Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Beer Sheva 84105, Israel
2 Novosibirsk State University ul. Pirogova 2 630090, Novosibirsk, Russia
3 Sobolev Institute of Mathematics Pr. Akad. Koptyuga 4 630090, Novosibirsk, Russia
Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 151-169.

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≤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≤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

Vladimir Golʼdshtein 1 ; Yaroslav Kopylov 2, 3

1 Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Beer Sheva 84105, Israel
2 Novosibirsk State University ul. Pirogova 2 630090, Novosibirsk, Russia
3 Sobolev Institute of Mathematics Pr. Akad. Koptyuga 4 630090, Novosibirsk, Russia 
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Vladimir Golʼdshtein; Yaroslav Kopylov. 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://ambp.centre-mersenne.org/articles/10.5802/ambp.359/

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