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Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory
June 3-19, 2009
Columbia University
New York, USA

Organizers
Abhijit Champanerkar (CSI, CUNY), Oliver Dasbach (LSU), Effie Kalfagianni (MSU), Ilya Kofman (CSI, CUNY), Walter Neumann (Barnard College, Columbia U.), Neal Stoltzfus (LSU)

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Hyperbolic manifolds, algebraic K-theory and the extended Bloch group
by
Christian Zickert
University of California, Berkeley

A closed hyperbolic 3-manifold M determines a fundamental class in the algebraic K-group K3ind(C). There is a regulator map K3ind(C)→ C/4Pi2Z, which evaluated on the fundamental class recovers the volume and Chern-Simons invariant of M. The definition of the K-groups are very abstract, and one is interested in more concrete models. The extended Bloch is such a model. It is isomorphic to K3ind(C) and has several interesting properties: Elements are easy to produce; the fundamental class of a hyperbolic manifold can be constructed explicitly; the regulator is given explicitly in terms of a polylogarithm.

Date received: June 2, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayy-32.