William P. Thurston

Learn More
This is an electronic edition of the 1980 notes distributed by Princeton University. The text was typed in T E X by Sheila Newbery, who also scanned the figures. Typos have been corrected (and probably others introduced), but otherwise no attempt has been made to update the contents. Genevieve Walsh compiled the index. Numbers on the right margin correspond(More)
This article was widely circulated as a preprint, about 12 years ago. At that time the Bulletin did not accept research announcements, and after a couple of attempts to publish it, I gave up, and the preprint did not find a home. I very soon saw that there were many ramifications of this theory, and I talked extensively about it in a number of places. One(More)
Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B to B , where B D H [ S 1 1 . The restriction to S 1 maps onto S 1 and gives an example of an equivariant S –filling(More)
THE CENTRAL objects of study in this paper are collections {C,, . . . , C,} of g disjoint circles on a closed orientable surface M of genus g, whose complement M-(C, u . . . U C,) is a 2g-punctured sphere. We call an isotopy class of such collections a cut system. Of course, any two cut systems are related by a diffeomorphism of M, by the classification of(More)
1. A conjectural picture of 3-manifolds. A major thrust of mathematics in the late 19th century, in which Poincaré had a large role, was the uniformization theory for Riemann surfaces: that every conformai structure on a closed oriented surface is represented by a Riemannian metric of constant curvature. For the typical case of negative Euler characteristic(More)
A rotation in a binary tree is a local restructuring that changes the tree into another tree. Rotations are useful in the design of tree-based data structures. The rotation distance between a pair of trees is the minimum number of rotations needed to convert one tree into the other. In this paper we establish a tight bound of In 6 on the maximum rotation(More)
The space of shapes of a polyhedron with given total angles less than 2π at each of its n vertices has a Kähler metric, locally isometric to complex hyperbolic space CH. The metric is not complete: collisions between vertices take place a finite distance from a nonsingular point. The metric completion is a complex hyperbolic conemanifold. In some(More)
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 &ed the final outcome; all that matters is that each transformation, when applied, is applied to the correct substructure. By taking advantage of this redundancy, we can develop an efficient encoding scheme for(More)