Abstract

We define an extended Bloch group for an arbitrary fieldF, and show that this group is naturally isomorphic toK3ind(F) ifF is a number field.This gives an explicit description ofK3ind(F) in terms of generators and relations. We give a concrete formula for the regulator, and derive concrete symbol expressions generating the torsion. As an application, we show that a hyperbolic 3-manifold with finite volume and invariant trace fieldk has a fundamental class[M] inK3ind(k)⊗ℤ[12]. IfM is closed,2[M] is well defined inK3ind(k), and ifM has cusps,8[M] is well defined inK3ind(k).

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