Bloch Invariants of Hyperbolic 3 - Manifoldswalter
نویسندگان
چکیده
We deene an invariant (M) of a nite 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. We show (M) lies in a subgroup of B(C) of nite Q-rank determined by the invariant trace eld of M. Moreover, the Chern-Simons invariant of M is determined modulo ra-tionals by (M). This leads to a simplicial formula and rationality results for the Chern Simons invariant which appear elsewhere. Generalizations of (M) are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of B(C).
منابع مشابه
Invariants from Triangulations of Hyperbolic 3 - Manifoldswalter
For any nite volume hyperbolic 3-manifold M we use ideal tri-angulation to deene an invariant (M) in the Bloch group B(C). It actually lies in the subgroup of B(C) determined by the invariant trace eld of M. The Chern-Simons invariant of M is determined modulo rationals by (M). This implies rationality and | assuming the Ramakrishnan conjecture | ir-rationality results for Chern Simons invariants.
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