Bloch invariants of hyperbolic 3-manifolds

Details Bloch invariants of hyperbolic 3-manifolds Bloch invariants of hyperbolic 3-manifolds

1997-12-04

arxiv.org/abs/math/9712224v1

Mathematics

Geometric Topology

25 pages. A slightly revised version will appear in Duke Math. J.

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Bloch invariants of hyperbolic 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bloch invariants of hyperbolic 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bloch invariants of hyperbolic 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-221179