Bloch invariants of hyperbolic 3-manifolds

Abstract

We define an invariant (M ) of a finite volume hyperbolic 3manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M . We show (M ) lies in a subgroup of B(C) of finite Q-rank determined by the invariant trace field of M . Moreover, the Chern-Simons invariant of M is determined modulo rationals by (M ). This leads to a simplicial formula and rationality results for the Chern Simons invariant which appear elsewhere.