Abstract
We prove that there are infinitely many non-homeomorphic hyperbolic knot complements for which Γi contains elements whose trace is an algebraic non-integer.
Mathematics Subject Classification:
Acknowledgments
We are very grateful to Shelly Harvey for pointing out the reference [Citation21] to us. We are also very grateful to Ken Baker, Neil Hoffman and Josh Howie for comments on an earlier version of this paper that led to the revised Section 7. We thank to Howie for allowing us to include his proof that the knot complements constructed in the proof of Theorem 1.1 contain a closed embedded essential surface that carries an essential simple closed curve isotopic to a meridian, as well as for the tangle decompositions shown in . Finally we thank the referees for several useful comments and suggestions.
Declaration of Interest
No potential conflict of interest was reported by the author(s).