Bloch invariants of hyperbolic 3-manifolds
Geometric Topology
2007-05-23 v1
Abstract
We define an invariant \beta(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. \beta(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 \beta(M). This leads to a simplicial formula and rationality results for the Chern Simons invariant which appear elsewhere. Generalizations of \beta(M) are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of B(C).
Keywords
Cite
@article{arxiv.math/9712224,
title = {Bloch invariants of hyperbolic 3-manifolds},
author = {Walter D. Neumann and Jun Yang},
journal= {arXiv preprint arXiv:math/9712224},
year = {2007}
}
Comments
25 pages. A slightly revised version will appear in Duke Math. J.