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

2002/11/04 by Stephane Baseilhac, Riccardo Benedetti
Mathematics · #math.GT #math.QA #msc:57M27 #msc:57Q15 #msc:57R20 #msc:20G42

paper · pdf

published as Geom. Topol. Monogr. 4 (2002) 13-28 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper2.abs.html

arxiv created 2002/11/04 · arxiv updated 2009/11/30

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.

Related

• QHI Theory, I: 3-Manifolds Scissors Congruence Classes and Quantum Hyperbolic Invariants
• A note on quantum 3-manifold invariants and hyperbolic volume
• QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters
• Quantum Hyperbolic Invariants Of 3-Manifolds With PSL(2,C)-Characters
• Hilbert's 3rd Problem and invariants of 3-manifolds