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

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

2011-01-14

arxiv.org/abs/1101.2742v1

Mathematics

Geometric Topology

30 pages, 8 figures

Scientific paper

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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