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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