298 citations · 844 across the 18 of their papers we have counts for
19 papers
Degree-d-invariant laminations
William P. Thurston, Hyungryul Baik, Yan Gao +4
Degree--invariant laminations of the disk model the dynamical action of a degree- polynomial; such a lamination defines an equivalence relation on that corresponds to d…
Entropy in Dimension One
William Thurston
This paper completely classifies which numbers arise as the topological entropy associated to postcritically finite self-maps of the unit interval. Specifically, a positive real nu…
Stabilization of Heegaard splittings
Joel Hass, Abigail Thompson, William Thurston
For each g greater than one there is a 3-manifold with two genus g Heegaard splittings that require g stabilizations to become equivalent. Previously known examples required at mos…
The absence of efficient dual pairs of spanning trees in planar graphs
T. R. Riley, W. P. Thurston
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G such that T and T* do not intersect. We show that it is not always pos…
Lower bounds on volumes of hyperbolic Haken 3-manifolds
Ian Agol, Nathan M. Dunfield, Peter A. Storm +1
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'…
Finite covers of random 3-manifolds
Nathan M. Dunfield, William P. Thurston
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…