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math.CO2005
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…
math.DG2005
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'…
math.GT2005
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…