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- Title
The extended Bloch group and algebraic K-theory.
- Authors
Zickert, Christian K.
- Abstract
We define an extended Bloch group for an arbitrary field F, and show that this group is naturally isomorphic to if F is a number field. This gives an explicit description of 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 field k has a fundamental class in . If M is closed, is well defined in , and if M has cusps, is well defined in .
- Subjects
TORSION products; K-theory; HOMOLOGICAL algebra; MANIFOLDS (Mathematics); FINITE volume method
- Publication
Journal für die Reine und Angewandte Mathematik, 2015, Vol 2015, Issue 704, p21
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2013-0055