Tameness conjecture

Tameness conjecture

In mathematics, the tameness conjecture states that every complete hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold, i.e. "topologically tame".

The conjecture was raised in the form of a question by Albert Marden, who proved that geometrically finite hyperbolic 3-manifolds are topologically tame. The conjecture is also called the Marden conjecture or tame ends conjecture.

The conjecture was proven in 2004 by Ian Agol, and independently, Danny Calegari and David Gabai, working together. This was the culmination of a series of breakthroughs by a dozen other mathematicians.

Further reading

*Dana Mackenzie, " [http://www.sciencemag.org/cgi/reprint/306/5705/2182.pdf Taming the hyperbolic jungle by pruning its unruly edges] ", Science, vol 306, 24 December 2004

References

*Ian Agol, "Tameness of hyperbolic 3-manifolds." [http://front.math.ucdavis.edu/math.GT/0405568 arXiv:math.GT/0405568]
*Calegari, Danny; Gabai, David, "Shrinkwrapping and the taming of hyperbolic 3-manifolds". J. Amer. Math. Soc. 19 (2006), no. 2, 385--446


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