Algorithmic detection and description of hyperbolic structures on closed 3{manifolds with solvable word problem
نویسنده
چکیده
We outline a rigorous algorithm, rst suggested by Casson, for determining whether a closed orientable 3-manifold M is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been given to solve the word problem in 1M . AMS Classi cation numbers Primary: 57M50
منابع مشابه
Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them
In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...
متن کاملThe Word Problem for 3-manifolds Built from Injective Handlebodies
This paper gives a proof that the fundamental group a class of closed orientable 3-manifolds constructed from three injective handlebodies has a solvable word problem. This is done by giving an algorithm, that terminates in bounded time, to decide if a closed curve in the manifold is null-homotopic.
متن کاملWord Hyperbolic Dehn Surgery
In the late 1970’s, Thurston dramatically changed the nature of 3-manifold theory with the introduction of his Geometrisation Conjecture, and by proving it in the case of Haken 3-manifolds [24]. The conjecture for general closed orientable 3-manifolds remains perhaps the most important unsolved problem in the subject. A weaker form of the conjecture [20] deals with the fundamental group of a cl...
متن کاملThurston’s Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3–manifolds
We show that the hyperbolic structure on a closed, orientable, hyperbolic 3–manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston’s spinning construction and a volume rigidity result attributed by Dunfield to Thurston, Gromov and Goldman. As an application, we show that this give...
متن کاملProblems around 3–manifolds
This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4–manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton–Perelman revolution. We give sets of problems based on the following themes; Minimal surfaces and hyperbolic geometry of 3–manifolds. In particular, how do minimal surfaces gi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002