Cohomologies of Sasakian groups and Sasakian solvmanifolds

Abstract

We show certain symmetry of the dimensions of cohomologies of the funda- mental groups of compact Sasakian manifolds by using the Hodge theory of twisted basic cohomology. As applications, we show that the polycyclic fundamental groups of compact Sasakian manifolds are virtually nilpotent and Sasakian solvmanifolds are finite quotients of Heisenberg nilmanifolds.

6 pages. To appear in Ann. Mat. Pura Appl

References in corpus (1)

• Hodge theory for twisted differentials

Cited by in corpus (3)

• A non-Sasakian Lefschetz K-contact manifold of Tievsky type
• A splitting theorem for compact Vaisman manifolds
• Extended simplicial rational Nomizu's Theorem