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A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

A smooth manifold M=(M,g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...