Tetrahedra of flags, volume and homology of SL.3/
By Nicolas Bergeron, Elisha Falbel, A. Antonin. 2011
48 citations recorded by the source corpus.
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 tetrahedral complexes considered in Falbel [6], and Falbel and Wang [8]. 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 and Zagier [18], Neumann [16] and Kabaya [15]. Our approach is very related to the work of Fock and Goncharov [9; 10]. 57M50; 57N10, 57R20
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/562b81380acb88537e62beb171e6250bf4325b88
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In Geometry and Topology
- Matthias Goerner
- Stavros Garoufalidis
- C. Zickert
- Martin Deraux
- Elisha Falbel
- Tudor Dimofte
- Sergei Gukov
- P. Sułkowski
In Mathematical Physics
Citations in the corpus
- Gluing equations for PGL(n, ℂ)–representations of 3–manifolds (2012, methodology): “Shape coordinates for n = 3 have been studied independently by Bergeron, Falbel and Guilloux [1].”
- The complex volume of SL(n,C)-representations of 3-manifolds (2011, unknown): “These include Bergeron-Falbel-Guilloux [2], Garoufalidis-Goerner-Zickert [15] and DimofteGabella-Goncharov [10].”
- COMPLEX HYPERBOLIC GEOMETRY OF THE FIGURE EIGHT KNOT (2013, background): “The authors wish to thank Christine Lescop, Antonin Guilloux, Julien Marché, Jean-Baptiste Meilhan, Jieyan Wang, Pierre Will and Maxime Wolff for useful discussions related to the paper.”