- nilmanifold
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A quotient space of a nilpotent Lie group modulo a closed subgroup, or (equivalently) a homogeneous space with a nilpotent Lie group acting transitively on it.
Wikipedia foundation.
Wikipedia foundation.
Nilmanifold — In mathematics, a nilmanifold is a differentiable manifold which has a transitive nilpotent group of diffeomorphisms acting on it. As such, a nilmanifold is an example of a homogeneous space and is diffeomorphic to the quotient space N / H, the… … Wikipedia
Rational homotopy theory — In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by Dennis Sullivan (1977) and Daniel Quillen (1969) … Wikipedia
Geometrization conjecture — Thurston s geometrization conjecture states that compact 3 manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3 manifolds of the uniformization theorem for… … Wikipedia
Almost flat manifold — In mathematics, a smooth compact manifold M is called almost flat if for any varepsilon>0 there is a Riemannian metric g varepsilon on M such that mbox{diam}(M,g varepsilon)le 1 and g varepsilon is varepsilon flat, i.e. for sectional curvature of … Wikipedia
List of mathematics articles (N) — NOTOC N N body problem N category N category number N connected space N dimensional sequential move puzzles N dimensional space N huge cardinal N jet N Mahlo cardinal N monoid N player game N set N skeleton N sphere N! conjecture Nabla symbol… … Wikipedia
Lefschetz manifold — In mathematics, a Lefschetz manifold is a particular kind of symplectic manifold.DefinitionsLet M be a (2n) dimensional smooth manifold. Each element: [omega] in H {DR}^2 (M) of the second de Rham cohomology space of M induces a map :L { [omega]… … Wikipedia
Solvmanifold — In mathematics, a solvmanifold is a homogeneous space of a connected solvable Lie group. It may also be characterized as a quotient of a connected solvable Lie group by a closed subgroup. (Some authors also require that the Lie group be simply… … Wikipedia
Aspherical space — In topology, an aspherical space is a topological space with all higher homotopy groups equal to {0}. If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is… … Wikipedia
Iwasawa manifold — In mathematics, in the field of differential geometry, an Iwasawa manifold is a compact quotient of a 3 dimensional complex Heisenberg group by a cocompact, discrete subgroup. An Iwasawa manifold is a nilmanifold, of real dimension 6.As a complex … Wikipedia
Collapsing manifold — For the concept in homotopy, see collapse (topology). In Riemannian geometry, a collapsing or collapsed manifold is an n dimensional manifold M that admits a sequence of Riemannian metrics gn, such that as n goes to infinity the manifold is close … Wikipedia