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Journal Articles Geometry & Topology Monographs Year : 2014

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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Dates and versions

hal-01370258 , version 1 (22-09-2016)

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Nicolas Bergeron, Elisha Falbel, Antonin Guilloux. Tetrahedra of flags, volume and homology of SL(3). Geometry & Topology Monographs, 2014, 18, ⟨10.2140/gt.2014.18.1911⟩. ⟨hal-01370258⟩
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