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The bigraded Rumin complex via differential forms

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 نشر من قبل Jeffrey Case
 تاريخ النشر 2021
  مجال البحث
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 تأليف Jeffrey S. Case




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We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. We also prove related Hodge decomposition theorems. Among many applications, we give a sharp upper bound on the dimension of the Kohn--Rossi groups $H^{0,q}(M^{2n+1})$, $1leq qleq n-1$, of a closed strictly pseudoconvex manifold with a contact form of nonnegative pseudohermitian Ricci curvature; we prove a sharp CR analogue of the Frolicher inequalities in terms of the second page of a natural spectral sequence; and we generalize the Lee class $mathcal{L}in H^1(M;mathscr{P})$ -- whose vanishing is necessary and sufficient for the existence of a pseudo-Einstein contact form -- to all nondegenerate orientable CR manifolds.



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