9 papers · 1 filter
The Computational Complexity of Knot Genus and Spanning Area
Ian Agol, Joel Hass, William P. Thurston
We investigate the computational complexity of some problems in three-dimensional topology and geometry. We show that the problem of determining a bound on the genus of a knot in a…
Lower bounds on volumes of hyperbolic Haken 3-manifolds
Ian Agol
In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds with various topological conditions. Let V_3 = 1.01494 denote the volume of a regular ideal simplex in hyp…
The size of spanning disks for polygonal curves
Joel Hass, Jack Snoeyink, William P. Thurston
Let be a closed polygonal curve in $\RR^3$ consisting of line segments. Assume that is unknotted, so that it is the boundary of an embedded disk in $\RR^3$. This paper…
Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary
William P. Thurston
This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifol…
Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
William P. Thurston
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian gr…
Minimal stretch maps between hyperbolic surfaces
William P. Thurston
This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps)…