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