Geometry & Topology Monographs 4 (2002) 13–28

DOI: 10.2140/gtm.2002.4.13

Abstract

This is a survey of our work on Quantum Hyperbolic Invariants (QHI) of 3–manifolds. We explain how the theory of scissors congruence classes is a powerful geometric framework for QHI and for a ‘Volume Conjecture’ to make sense.

Keywords

volume conjecture, hyperbolic 3–manifolds, scissors congruence classes, state sum invariants, 6j–symbols, quantum dilogarithm

Mathematical Subject Classification

Primary: 57M27, 57Q15

Secondary: 20G42, 57R20

References

Publication

Received: 27 November 2001
Revised: 17 April 2002
Accepted: 22 July 2002
Published: 19 September 2002

Authors