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Tetrahedra of flags, volume and homology of SL(3)

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arxiv 1101.2742 v2 pith:6DKYRGFL submitted 2011-01-14 math.GT math.KT

Tetrahedra of flags, volume and homology of SL(3)

Nicolas Bergeron , Elisha Falbel , Antonin Guilloux Antonin This is my paper
classification math.GT math.KT
keywords volumetetrahedracomplexesapproachbelongsblochclassicaldefine
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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 tetrahedra complexes. We describe when this volume belongs to the Bloch group. In doing so, we recover and generalize results of Neumann-Zagier, Neumann, and Kabaya. Our approach is very related to the work of Fock and Goncharov.

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