Trace fields and commensurability of link complements

Details Trace fields and commensurability of link complements Trace fields and commensurability of link complements

2007-08-08

arxiv.org/abs/0708.1184v2

Mathematics

Geometric Topology

29 pages, 9 figures; added emails and affiliations for authors

Scientific paper

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.

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