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Generalized orientations and the Bloch invariant

Michel Matthey·Wolfgang Pitsch·Jerome Scherer
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Abstract

For compact hyperbolic 3-manifolds we lift the Bloch invariant defined by Neumann and Yang to an integral class in K_3(C) Applying the Borel and the Bloch regulators, one gets back the volume and the Chern-Simons invariant of the manifold. We also discuss the non-compact case, in which there appears a Z/2-ambiguity.

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Michel Matthey, Wolfgang Pitsch, Jerome Scherer. 2006-07-20. Generalized orientations and the Bloch invariant. https://arxiv.org/abs/math/0607496

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