Koszul–Sullivan Models and the Cohomology of Certain Solvmanifolds

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In this paper we develop a technique of working with graded differential algebra models of solvmanifolds, overcoming the main difficulty arising from the ‘non-nilpotency’ of the corresponding Mostow fibrations. A graded differential model for solvmanifolds of the form G/Γ with G=R⋊ϕN is presented (N is a nilpotent Lie group, G is a semi-direct product). As an application, we prove the Benson–Gordon conjecture in dimension four.