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QHI, 3–manifolds scissors congruence classes and the
volume conjecture
Stephane Baseilhac and Riccardo Benedetti
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Geometry & Topology Monographs 4
(2002) 13–28
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Abstract
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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.
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Keywords
volume conjecture, hyperbolic
3–manifolds, scissors congruence classes, state sum
invariants, 6j–symbols, quantum dilogarithm
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Mathematical Subject Classification
Primary: 57M27, 57Q15
Secondary: 20G42, 57R20
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Publication
Received: 27 November 2001
Revised: 17 April 2002
Accepted: 22 July 2002
Published: 19 September 2002
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