Bloch invariants of hyperbolic 3-manifolds
Walter D. Neumann, Jun Yang
Abstract
We define an invariant β(M) of a finite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. β(M) lies in a subgroup of () of finite -rank determined by the invariant trace field of M. Moreover, the Chern-Simons invariant of M is determined modulo rationals by β(M). This leads to a simplicial formula and rationality results for the Chern Simons invariant which appear elsewhere. Generalizations of β(M) are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of B(C).
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