$L_{p,q}$-cohomology of warped cylinders

Kopylov, Yaroslav

Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 321-338.

On généralise quelques résultats par Gol${}^{\prime }$dshtein, Kuz${}^{\prime }$minov et Shvedov sur la cohomologie $L_p$ des cylindres tordus à cohomologie $L_{p,q}$ pour $p\ne q$. Comme application, on établit des conditions suffisantes pour la non-nullité de la torsion $L_{p,q}$ d’une surface de révolution.

We extend some results by Gol${}^{\prime }$dshtein, Kuz${}^{\prime }$minov, and Shvedov about the $L_p$-cohomology of warped cylinders to $L_{p,q}$-cohomology for $p\ne q$. As an application, we establish some sufficient conditions for the nontriviality of the $L_{p,q}$-torsion of a surface of revolution.

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