Quakebend deformations in complex hyperbolic quasi-Fuchsian space. (English) Zbl 1153.30038
The main object of study in this paper is the set of discrete representations of a surface group into \(SU(2,1)\). This defines a complex hyperbolic quasi–Fuchsian structure on the surface which is isomorphic to a disc bundle over the surface. The problem is to understand the set of deformations of this structure. This is done by a class of deformations known as quakebends. The author constructs curves associated with this class of deformation emanating from representations into \(SO(2,1)\). For any representation the author can show this process produces an open set of representations. He also proves a generalization of the Wolpert-Kerkoff formula.
Reviewer: Samuel James Patterson (Göttingen)
MSC:
| 30F60 | Teichmüller theory for Riemann surfaces |
| 30F35 | Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) |
| 32M05 | Complex Lie groups, group actions on complex spaces |
Keywords:
complex hyperbolic space; surface groups; Teichmüller space; quakebend deformations; Wolpert-Kerkoff formulaReferences:
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