Ideal triangulations of finite volume hyperbolic 3-manifolds
نویسنده
چکیده
Any non compact finite volume hyperbolic 3-manifold has a finite cover which admits a nondegenerate ideal triangulation. As an application, we show that the volume of those manifolds is always a critical value of a function defined from the Lobachevskii function.
منابع مشابه
An Inequality for Polyhedra and Ideal Triangulations of Cusped Hyperbolic 3-manifolds
It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let M be a hyperbolic 3-manifold obtained by identifying the faces of n convex ideal polyhedra P1, . . . , Pn. If the faces of P1, . . . , Pn−1 are glued to Pn, then M can be decomposed into ideal tetrahedra by subdividing the ...
متن کاملThe cusped hyperbolic census is complete
From its creation in 1989 through subsequent extensions, the widely-used “SnapPea census” now aims to represent all cusped finite-volume hyperbolic 3-manifolds that can be obtained from ≤ 8 ideal tetrahedra. Its construction, however, has relied on inexact computations and some unproven (though reasonable) assumptions, and so its completeness was never guaranteed. For the first time, we prove h...
متن کاملInvariants from Triangulations of Hyperbolic 3-manifolds
For any finite volume hyperbolic 3-manifold M we use ideal triangulation to define an invariant β(M) in the Bloch group B(C ). It actually lies in the subgroup of B(C ) determined by the invariant trace field of M . The Chern-Simons invariant of M is determined modulo rationals by β(M). This implies rationality and — assuming the Ramakrishnan conjecture — irrationality results for Chern Simons ...
متن کاملGeodesic Ideal Triangulations Exist Virtually
It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability ...
متن کاملConstruction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston’s approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks’ tilt formula algorithm, which computes th...
متن کامل