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Invariants from Triangulations of Hyperbolic 3-Manifolds
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## Invariants from triangulations of hyperbolic 3-manifolds

### Walter D. Neumann and Jun Yang

**Abstract.**
For any finite volume hyperbolic 3-manifold $M$ we use ideal
triangulation to define an invariant $\beta(M)$ in the Bloch group
$\B(\C)$. It actually lies in the subgroup of $\B(\C)$ 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.

*Copyright American Mathematical Society 1995
*

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#### Article Info

- ERA Amer. Math. Soc.
**01** (1995), pp. 72-79
- Publisher Identifier: S 1079-6762(95)02003-7
- 1991
*Mathematics Subject Classification*. 57M50, 30F40; 19E99, 22E40, 57R20.
- Received by the editors May 5, 1995, and, in revised form, July 19, 1995
- Comments

**Walter D. Neumann**

Department of Mathematics

The University of
Melbourne

Carlton, Vic 3052

Australia

*E-mail address:* `neumann@maths.mu.oz.au`

**Jun Yang**

Department of Mathematics

Duke University

Durham NC 27707

*E-mail address:* `yang@math.duke.edu`

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