Bloch Invariants of Hyperbolic 3-manifolds
نویسندگان
چکیده
We define an invariant β(M) of a finite volume hyperbolic 3manifoldM in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M . We show β(M) lies in a subgroup of B(C) of finite Q-rank determined by the invariant trace field of M . Moreover, the Chern-Simons invariant of M is determined modulo rationals by β(M). This leads to a simplicial formula and rationality results for the Chern Simons invariant which appear elsewhere. Generalizations of β(M) are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of B(C).
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For any finite volume hyperbolic 3-manifold M we use ideal triangulation to define an invariant β(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 β(M). This implies rationality and — assuming the Ramakrishnan conjecture — irrationality results for Chern Simons ...
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