nLab nilmanifold

Definition

A nilmanifold is a differentiable manifold which admits a smooth transitive action by a nilpotent Lie group $G$, hence which is diffeomorphic to a coset space (homogeneous space) $G/\Gamma$ for $\Gamma \subset G$ a closed subgroup of a nilpotent Lie group.

Examples

• Heisenberg manifold

References

See also:

• Wikipedia: Nilmanifold

• Grokipedia: Nilmanifold

On minimal Sullivan models of nilmanifolds:

• Keizo Hasegawa: Minimal models of nilmanifolds, Amer. Math. Soc. 106 (1989) 65-71 [doi:10.1090/S0002-9939-1989-0946638-X, pdf]