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Electronic Research Announcements

ISSN 1079-6762



Invariants from triangulations of hyperbolic 3-manifolds

Authors: Walter D. Neumann and Jun Yang
Journal: Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 72-79
MSC (1991): Primary 57M50, 30F40, 19E99, 22E40, 57R20
MathSciNet review: 1350682
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Abstract: For any finite volume hyperbolic 3-manifold $M$ we use ideal triangulation to define an invariant $\beta (M)$ in the Bloch group $\mathcal {B}(\mathbb {C})$. It actually lies in the subgroup of $\mathcal {B}(\mathbb {C})$ determined by the invariant trace field of $M$. The Chern-Simons invariant of $M$ is determined modulo rationals by $\beta (M)$. This implies rationality and — assuming the Ramakrishnan conjecture — irrationality results for Chern Simons invariants.

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Additional Information

Walter D. Neumann
Affiliation: Department of Mathematics The University of Melbourne Carlton, Vic 3052 Australia

Jun Yang
Affiliation: Department of Mathematics Duke University Durham NC 27707

Received by editor(s): May 5, 1995
Received by editor(s) in revised form: July 19, 1995
Article copyright: © Copyright 1995 American Mathematical Society