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Minimal models of nilmanifolds

1989; American Mathematical Society; Volume: 106; Issue: 1 Linguagem: Inglês

10.1090/s0002-9939-1989-0946638-x

1088-6826

Keizo Hasegawa,

Homotopy and Cohomology in Algebraic Topology

In this paper we first determine minimal models of nilmanifolds associated with given rational nilpotent Lie algebras. Then we study some properties of nilmanifolds through their associated Lie algebras and minimal models. In particular, we will see that a minimal model of a nilmanifold is formal if and only if it is a torus, and thus a non-toral nilmanifold has no complex structure which is birationally isomorphic to a Kähler manifold.