Tetrahedra of flags, volume and homology of SL(3)
Abstract
In the paper we define a " volume " for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrahe-dra complexes considered in [4, 6]. We describe when this volume belongs to the Bloch group and more generally describe a variation formula in terms of boundary data. In doing so, we recover and generalize results of Neumann-Zagier [13], Neumann [11], and Kabaya [10]. Our approach is very related to the work of Fock and Goncharov [7, 8].
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