- Tameness conjecture
In
mathematics , the tameness conjecture states that every completehyperbolic 3-manifold with finitely generatedfundamental 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 andDavid 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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