On solvmanifolds and a conjecture of Benson and Gordon from the hamiltonian viewpoint

Abstract: In this work we prove a theorem which shows that under some mild restrictions on a solvmanifold $\scriptstyle G/\Gamma$ the existence of a Kähler structure on it forces $\scriptstyle G$ to be metabelian and, hence this result is only `one-step' removed from the original Benson-Gordon conjecture. Applications and examples are discussed. The proof develops the `hamiltonian' idea of D. McDuff which appeared in her proof of the same conjecture for nilmanifolds [22] as well as ideas of G. Lupton and J. Oprea contained in [20].

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