On the trace fields of hyperbolic Dehn fillings

Abstract

Assuming Lehmer's conjecture, we estimate the degree of the trace field $K(M_{p/q})$ of a hyperbolic Dehn-filling $M_{p/q}$ of a 1-cusped hyperbolic 3-manifold $M$ by $$\frac{1}{C}(\max \{|p|,|q|\})\le \text{deg }K(M_{p/q})\le C(\max \{|p|,|q|\})$$ where $C=C_M$ is a constant that depends on $M$.

22 pages. Final version. To appear in the Bulletin of the London Math. Soc