Geometric structures associated to triangulations as fixed point sets of involutions

DOI10.1016/j.topol.2006.10.006zbMath1112.57002OpenAlexW2059805604MaRDI QIDQ870234

Elisha Falbel

Publication date: 12 March 2007

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2006.10.006

zbMATH Keywords

triangulationhyperbolic structurecross ratioCR structureideal triangulation

Mathematics Subject Classification ID

Related Items (13)

Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1 ⋮ Paired CR structures and the example of Falbel's cross-ratio variety ⋮ On Fenchel–Nielsen Coordinates of Surface Group Representations into SU(3,1) ⋮ Quaternionic hyperbolic Fenchel-Nielsen coordinates ⋮ Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1 ⋮ The \(\mathrm{PU}(2,1)\) configuration space of four points in \(S^3\) and the cross-ratio variety ⋮ The moduli space of complex geodesics in the complex hyperbolic plane ⋮ The moduli space of points in the boundary of complex hyperbolic space ⋮ Complex lines in complex hyperbolic space \({H_{\mathbb{C}}^{2}}\) ⋮ On the moduli space of quadruples of points in the boundary of complex hyperbolic space ⋮ Conjugation orbits of loxodromic pairs in \(\mathrm{SU}(n, 1)\) ⋮ On conjugation orbits of semisimple pairs in rank one ⋮ McShane's identity in rank one symmetric spaces

Cites Work

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• The complex cross ratio on the Heisenberg group
• Real hyperbolic on the outside, complex hyperbolic on the inside
• Lagrangian decomposability of some two-generator subgroups of \(\text{PU}(2,1)\).
• Extended Bloch group and the Cheeger-Chern-Simons class
• Classical and quantum dilogarithmic invariants of flat \(\text{PSL}(2,\mathbb C)\)-bundles over 3-manifolds

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