Trace fields and commensurability of link complements
Abstract
Description
This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifolds with the same property. We also show that the two-component link complements above have integral traces, but each has a mutant with a nonintegral trace.
29 pages, 9 figures; added emails and affiliations for authors
29 pages, 9 figures; added emails and affiliations for authors