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Invariants from triangulations of hyperbolic 3-manifolds. (English) Zbl 0851.57013

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.
Reviewer: W.D.Neumann

MSC:

57M50 General geometric structures on low-dimensional manifolds
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
19E99 \(K\)-theory in geometry
22E40 Discrete subgroups of Lie groups
57R20 Characteristic classes and numbers in differential topology

Software:

SnapPea
Full Text: DOI EuDML

References:

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