Lower bounds on volumes of hyperbolic Haken 3-manifolds (2005)
Agol, Ian, Dunfield, Nathan M., Storm, Peter A., Thurston, William P.
We prove a volume inequality for 3-manifolds having C^0 metrics "bent" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on Ricci...
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of...
Finite covers of random 3-manifolds (2005)
Dunfield, Nathan M., Thurston, William P.
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which...
The virtual Haken conjecture: Experiments and examples (2003)
Dunfield, Nathan M., Thurston, William P.
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is...
Area Inequalities for Embedded Disks Spanning Unknotted Curves (2003)
Hass, Joel, Lagarias, Jeffrey C., Thurston, William P.
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 length L of the curve...
The virtual Haken conjecture: Experiments and examples (2002)
Dunfield, Nathan M, Thurston, William P
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is...
The Computational Complexity of Knot Genus and Spanning Area (2002)
Agol, Ian, Hass, Joel, Thurston, William P.
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 3-manifold, is...
On Three-Dimensional Space Groups (1999)
Conway, John, Friedrichs, Olaf Delgado, Huson, Daniel H., Thurston, William P.
An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible....
The size of spanning disks for polygonal curves (1999)
Hass, Joel, Snoeyink, Jack, Thurston, William P.
Let $K$ be a closed polygonal curve in $\RR^3$ consisting of $n$ line segments. Assume that $K$ is unknotted, so that it is the boundary of an embedded disk in $\RR^3$. This paper considers the...
Short Encodings of Evolving Structures, (1998)
Sleator, Daniel D., Tarjan, Robert E., Thurston, William P.
A derivation in a transformational system such as a graph grammar may be redundant in the sense that the exact order of the transformations may not affect the final outcome; all that matters is that...
The Symbolic Dynamics of Tiling the Integers (1998)
Coven, Ethan M., Geller, William, Silberger, Sylvia, Thurston, William P.
A finite collection $P$ of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of $P$. We associate with such a tiling a doubly infinite...
Shapes of polyhedra and triangulations of the sphere (1998)
The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not...
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 manifolds with...
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 groups whose...
Minimal stretch maps between hyperbolic surfaces (1998)
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) and geodesics for...
Hyperbolic Structures on 3-manifolds, I: Deformation of acylindrical manifolds (1998)
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were...
The size of spanning disks for PL Knots. (1998)
Joel Hass, Jack Snoeyink, William P. Thurston
For each integer n ? 1 we construct a closed unknotted PL curve Kn in R 3 having less than 33n edges with the property that any PL triangluated disk spanning the curve contains at least 2 n...
Three-manifolds, Foliations and Circles, I (1997)
This paper investigates certain foliations of three-manifolds that are hybrids of fibrations over the circle with foliated circle bundles over surfaces: a 3-manifold slithers around the circle when...
On proof and progress in mathematics (1994)
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of...
Computer Science, Daniel Barbara, Frank Pittelli, Hector Garcia-molina, Hector Garcia-molina, Daniel D. Sleator, ...
s of all technical reports published by the Department of Computer Science between 1985 and 1991 are listed below. Some of these reports are available for anonymous ftp or can be purchased from the...