Tame manifold - Misplaced Pages

Not to be confused with Tame topology.

In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold $M$ is called tame if it is homeomorphic to a compact manifold with a closed subset of the boundary removed.

The Whitehead manifold is an example of a contractible manifold that is not tame.

References

Gabai, David (2009), "Hyperbolic geometry and 3-manifold topology", in Mrowka, Tomasz S.; Ozsváth, Peter S. (eds.), Low dimensional topology, IAS/Park City Math. Ser., vol. 15, Providence, R.I.: Amer. Math. Soc., pp. 73–103, ISBN 978-0-8218-4766-4, MR 2503493
Marden, Albert (2007), Outer circles, Cambridge University Press, doi:10.1017/CBO9780511618918, ISBN 978-0-521-83974-7, MR 2355387
Tucker, Thomas W. (1974), "Non-compact 3-manifolds and the missing-boundary problem", Topology, 13 (3): 267–273, doi:10.1016/0040-9383(74)90019-6, ISSN 0040-9383, MR 0353317

Basic concepts

Main results (list)

Types of
manifolds

Vectors	Distribution Lie bracket Pushforward Tangent space bundle Torsion Vector field Vector flow
Covectors	Closed/Exact Covariant derivative Cotangent space bundle De Rham cohomology Differential form Vector-valued Exterior derivative Interior product Pullback Ricci curvature flow Riemann curvature tensor Tensor field density Volume form Wedge product
Bundles	Adjoint Affine Associated Cotangent Dual Fiber (Co) Fibration Jet Lie algebra (Stable) Normal Principal Spinor Subbundle Tangent Tensor Vector
Connections	Affine Cartan Ehresmann Form Generalized Koszul Levi-Civita Principal Vector Parallel transport

Generalizations

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