Abstract
Let M be a hyperbolic 3-manifold and k(M) the invariant trace field of M. It is known that that if M is commensurably amphicheirable, the k(M) = k(M), where k(M) is the complex conjugate of k(M). In this paper, we show that the reverse is not true in general. We construct commensurably non amphicheirable hyperbolic 3-manifolds Mk(k = 3,4,…) and show that k(Mk) = k(Mk). We also show that this set containes infinitely many commensurability classes.
