Add to ORKGIf a hyperbolic link has a prime alternating diagram D, then we show that the link complement's volume can be estimated directly from D. We define a very elementary invariant of the diagram D, its twist number t(D), and show that the volume lies between v_3(t(D) - 2)/2 and v_3(16t(D) - 16), where v_3 is the volume of a regular hyperbolic ideal 3-simplex. As a consequence, the set of all hyperbolic alternating and augmented alternating link complements is a closed subset of the space of all complete finite volume hyperbolic 3-manifolds, in the geometric topology. The appendix by Ian Agol and Dylan Thurston, which was written after the first version of this paper was distributed, improves the upper bound on volume to v_3(10t(D) - 10). In addi...
Since the 1980s, it has been known that essential surfaces in alternating link complements can be is...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-...
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-...
The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a ...
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in ...
For a hyperbolic link in the 3-sphere, the hyperbolic volume of its complement is an interesting and...
For a hyperbolic link in the 3-sphere, the hyperbolic volume of its complement is an interesting and...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Abstract. We give a refined upper bound for the hyperbolic volume of an alternating link in terms of...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic...
Since the 1980s, it has been known that essential surfaces in alternating link complements can be is...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-...
We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-...
The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a ...
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in ...
For a hyperbolic link in the 3-sphere, the hyperbolic volume of its complement is an interesting and...
For a hyperbolic link in the 3-sphere, the hyperbolic volume of its complement is an interesting and...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Recently, the explicit volume formulae for hyperbolic cone-manifolds, whose underlying space is the ...
Abstract. We give a refined upper bound for the hyperbolic volume of an alternating link in terms of...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic...
Since the 1980s, it has been known that essential surfaces in alternating link complements can be is...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...
A finite-volume hyperbolic 3–manifold geometrically bounds if it is the geodesic boundary of a finit...