In mathematics, the tameness theorem states that every complete hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, in other words homeomorphic to the interior of a compact 3-manifold.
The tameness theorem was conjectured by Marden (1974). It was proved by Agol (2004) and, independently, by Danny Calegari and David Gabai. It is one of the fundamental properties of geometrically infinite hyperbolic 3-manifolds, together with the density theorem for Kleinian groups and the ending lamination theorem.
It also implies the Ahlfors measure conjecture.
mathematics, the tamenesstheorem states that every complete hyperbolic 3-manifold with finitely generated fundamental group is topologically tame, in other...
lamination conjecture for Kleinian surface groups. In view of the Tamenesstheorem this implies the ending lamination conjecture for all finitely generated...
that is not tame. Closed manifold – compact manifold without boundaryPages displaying wikidata descriptions as a fallback Tamenesstheorem Gabai, David...
The density conjecture was finally proved using the tamenesstheorem and the ending lamination theorem by Namazi & Souto (2012) and Ohshika (2011). Bers...
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to...
the University of Illinois at Chicago. In 2004, Agol proved the Marden tameness conjecture, a conjecture of Albert Marden. It states that a hyperbolic...
logic, a tame abstract elementary class is an abstract elementary class (AEC) which satisfies a locality property for types called tameness. Even though...
topologically tame groups, by showing that a topologically tame Kleinian group is geometrically tame, so the Ahlfors conjecture follows from Marden's tameness conjecture...
maximal tamely ramified extension of K ( ( T ) ) {\displaystyle K(\!(T)\!)} . Similarly to the case of algebraic closure, there is an analogous theorem for...
no maximal models and tameness as the uncountable analog to Fraïssé's constructions (with VanDieren), a stability spectrum theorem and the existence of...
For example, the tameness requirement can be replaced by the much weaker condition, continuous. The proof of the structure theorem relies on the base...
as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...
ambient space is the three-sphere no information is lost: the Gordon–Luecke theorem states that a knot is determined by its complement. That is, if K and K′...
is tame ramification. In terms of the discriminant D of L, and taking still K = Q, no prime p must divide D to the power p. Then Noether's theorem states...
optional stopping theorem is an important result in this context. Stopping times are also frequently applied in mathematical proofs to “tame the continuum...
of K {\displaystyle K} . (This is stronger than the primitive element theorem.) Then, for each integer i ≥ − 1 {\displaystyle i\geq -1} , we define G...
object or to take the last object. Nim is fundamental to the Sprague–Grundy theorem, which essentially says that every impartial game is equivalent to a nim...
odd-order theorem uses "tamely embedded subsets" and an isometry from class functions with support on a tamely embedded subset. If K1 is a tamely embedded...
(Frederick V. Henle and James M. Henle, 2008) Tameness conjecture (Ian Agol, 2004) Ending lamination theorem (Jeffrey F. Brock, Richard D. Canary, Yair N...
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