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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
Email: neumann@maths.mu.oz.au

Jun Yang
Affiliation: Department of Mathematics Duke University Durham NC 27707
Email: yang@math.duke.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-95-02003-8
PII: S 1079-6762(95)02003-8
Received by editor(s): May 5, 1995
Received by editor(s) in revised form: July 19, 1995
Article copyright: © Copyright 1995 American Mathematical Society



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