QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters

Details QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters

2002-11-04

arxiv.org/abs/math/0211061v2

Mathematics

Geometric Topology

23 pages, 2 figures. The way we refer to W.Neumann's earlier works is modified. The rest of the paper is unchanged

Scientific paper

We give parallel constructions of an invariant R(W,f), based on the classical Rogers dilogarithm, and of quantum hyperbolic invariants (QHI), based on the Faddeev-Kashaev quantum dilogarithms, for flat PSL(2,C)-bundles f over closed oriented 3-manifolds W. All these invariants are explicitely computed as a sum or state sums over the same hyperbolic ideal tetrahedra of the idealization of any fixed simplicial 1-cocycle description of (W,f) of a special kind, called a D-triangulation. R(W,f) recovers the volume and the Chern-Simons invariant of f, and we conjecture that it determines the semi-classical limit of the QHI.

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