3 papers
math.GT2013
Denominators and Differences of Boundary Slopes for (1,1)-Knots
Jason Callahan
We show that every nonzero integer occurs in the denominator of a boundary slope for infinitely many (1,1)-knots and that infinitely many (1,1)-knots have boundary slopes of arbitr…
math.GT2009
Jørgensen Number and Arithmeticity
Jason Callahan
A Jørgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in Jørgensen's Inequality. This paper shows that the only torsio…
math.GT2008
Conjugate Generators of Knot and Link Groups
Jason Callahan
This note shows that if two elements of equal trace (e.g., conjugate elements) generate an arithmetic two-bridge knot or link group, then the elements are parabolic. This includes…