QHI Theory, II: Dilogarithmic and Quantum Hyperbolic Invariants of 3-Manifolds with PSL(2,C)-Characters
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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.
23 pages, 2 figures. The way we refer to W.Neumann's earlier works is modified. The rest of the paper is unchanged
23 pages, 2 figures. The way we refer to W.Neumann's earlier works is modified. The rest of the paper is unchanged