Nilmanifold
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In mathematics, a nilmanifold is the quotient space of a nilpotent Lie group modulo a closed subgroup.
[edit] Examples
The standard two-dimensional torus T2 is a nilmanifold, it being a quotient of R2 (a nilpotent Lie group under addition) by the integer lattice. In general, the torus in any dimension is a nilmanifold, it being a quotient of Rn by the integer lattice. The tori in dimensions 1 and 2 are the unique compact nilmanifolds of their dimensions.
The Heisenberg group is a nilpotent Lie algebra, and a quotient by its "integer lattice" gives a 3-dimensional nilmanifold not homeomorphic to T3, called "baby nil".
[edit] Generalizations
A parallel construction based on solvable Lie groups produces a class of spaces called solvmanifolds.
