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We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold and the -cohomology of that manifold. The -cohomology of is defined to be the quotient of the space of closed differential forms in modulo the exact forms which are exterior differentials of forms in .
Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti
Aude Billard, Iason Batzianoulis, Anqing Duan