192 citations · 222 across the 4 of their papers we have counts for
7 papers · 1 filter
Systoles of hyperbolic 4-manifolds
Ian Agol
We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.
Transcendental ending laminations
Ian Agol
Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν_-,ν_+). In this note, we show that there are ending laminations ν_+ such that for a…
Tameness of hyperbolic 3-manifolds
Ian Agol
We show that hyperbolic 3-manifolds with finitely generated fundamental group are tame, that is the ends are products. We actually work in slightly greater generality with pinched…
Small 3-manifolds of large genus
Ian Agol
We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary para…
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…