Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 2, pages 13--28.

QHI, 3-manifolds scissors congruence classes and the volume conjecture

Stephane Baseilhac, Riccardo Benedetti

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

AMS subject classification. Primary: 57M27, 57Q15. Secondary: 57R20, 20G42.

E-print: arXiv:math.GT/0211053

Submitted to GT on 27 November 2001. (Revised 17 April 2002.) Paper accepted 22 July 2002. Paper published 19 September 2002.

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Stephane Baseilhac, Riccardo Benedetti
Dipartimento di Matematica, Universita di Pisa
Via F. Buonarroti, 2, I-56127 Pisa, Italy

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