11 papers
Area Inequalities for Embedded Disks Spanning Unknotted Curves
Joel Hass, Jeffrey C. Lagarias, William P. Thurston
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the lengt…
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…
The Symbolic Dynamics of Tiling the Integers
Ethan M. Coven, William Geller, Sylvia Silberger +1
A finite collection of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of . We associate with such a tiling a d…
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…