42 citations · 434 across the 64 of their papers we have counts for
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Independence of volume and genus bridge numbers
Jessica S. Purcell, Alexander Zupan
A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus. Heegaard surfaces and bridge sur…
Density spectra for knots
Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell
We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this stud…
Volume bounds for weaving knots
Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We pr…
Geometry of planar surfaces and exceptional fillings
Neil R. Hoffman, Jessica S. Purcell
If a hyperbolic 3-manifold admits an exceptional Dehn filling, then the length of the slope of that Dehn filling is known to be at most six. However, the bound of six appears to be…
Volumes of Montesinos links
Kathleen Finlinson, Jessica S. Purcell
We show that the volume of any Montesinos link can be bounded above and below in terms of the combinatorics of its diagram. This was known for Montesinos links with at most two tan…