Complex hyperbolic triangle groups
By Richard Evan Schwartz. 2003
97 citations recorded by the source corpus.
The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry. In this paper I will discuss some recent progress that has been made on complex hyperbolic deformations of the modular group and, more generally, triangle groups. These are some of the simplest nontrivial complex hyperbolic discrete groups. In particular, I will talk about my recent discovery of a closed real hyperbolic 3-manifold which appears as the manifold at infinity for a complex hyperbolic discrete group.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e343fd4f5281cf027f05875b06a97b808c12426a
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In Geometry and Topology
- William M. Goldman
- John R. Parker
- Martin Deraux
- Julien Paupert
- Michael Kapovich
- Anna Wienhard
- J. Porti
- B. Leeb
In Mathematical Physics
- William M. Goldman
- Martin Deraux
- Julien Paupert
- John R. Parker
- Michael Kapovich
- Anna Wienhard
- B. Leeb
- Ludovic Marquis
Citations in the corpus
- KLEINIAN GROUPS IN HIGHER DIMENSIONS (2007, background): “Therefore, if Ωi is simply-connected, then Ωi is contractible.”
- New non-arithmetic complex hyperbolic lattices (2014, background): “p with a given angle/trace pair to exist (see the discussion in [PP09]); when it exists, we denote the corresponding group by Γ(ψ,τ). Following previous work on complex reflection groups (see [Mos80], [Sch02], [Der06], [Tho10]), one expects such groups to be lattices only when well-chosen short words”
- Locally Homogeneous Geometric Manifolds (2010, background): “Other interesting examples of spherical CR-structures on 3- manifolds have been constructed by Schwartz [144, 145, 146], Falbel [57], Gusevskii, Parker [137], Parker-Platis [138].”