Tame manifold

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., Low dimensional topology, IAS/Park City Math. Ser., 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. an International Journal of Mathematics, 13 (3): 267–273, doi:10.1016/0040-9383(74)90019-6, ISSN 0040-9383, MR 0353317