Infinitely many knots with non-integral trace

Abstract

We prove that there are infinitely many non-homeomorphic hyperbolic knot complements $S^3\setminus K_i={\mathbb{H}}^3/{\Gamma }_i$ for which ${\Gamma }_i$ contains elements whose trace is an algebraic non-integer.

15 pages, 6 figures; v2 includes answers to some questions in section 8 raised in v1