Sullivan's theory of models can be used to get topological invariants of manifolds that are stronger than the de Rham cohomology ring. One defines a model for a manifold as a commutative differential graded algebra (CDGA) quasi-isomorphic to the algebra of differential forms. It is known that the minimal model of a compact nilmanifold is given by the Chevalley-Eilenberg complex of the corresponding Lie algebra. Recently, in his PhD thesis A. Tievsky constructed a finite-dimensional model of a compact Sasakian manifold. Comparing models for nilmanifolds and Sasakian manifolds, we give a classification of compact Sasakian nilmanifolds. This is joint work with B. Cappelletti-Montano, J. C. Marrero and I. Yudin.
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