Geometric structures associated to triangulations as fixed point sets of involutions
TLDR
In this paper, it was shown that hyperbolic structures and spherical CR structures on a 3D manifold are contained in fixed point sets of a larger class of structures associated to a triangulation of the manifold.About:
This article is published in Topology and its Applications.The article was published on 2007-03-15 and is currently open access. It has received 35 citations till now. The article focuses on the topics: Stable manifold theorem & Hyperbolic equilibrium point.read more
Citations
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Complex hyperbolic Fenchel–Nielsen coordinates
John R. Parker,Ioannis D. Platis +1 more
TL;DR: In this paper, the authors give global real analytic coordinates on a subset of the representation variety that contains the quasi-Fuchsian representations, which are a natural generalisation of Fenchel-Nielsen coordinates on the Teichmuller space of π 1 ( Σ ) and complex FenchelýnnsýnsÕ on the (classical) quasi Fuchsian space of Σ.
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On the moduli space of quadruples of points in the boundary of complex hyperbolic space
Heleno Cunha,Nikolay Gusevskii +1 more
TL;DR: In this article, the authors considered the moduli space of ordered quadruples of distinct points in the boundary of complex hyperbolic n-space, up to its holomorphic isometry group PU(n, 1).
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The PU(2,1) configuration space of four points in S 3 and the cross-ratio variety
Elisha Falbel,Ioannis D. Platis +1 more
TL;DR: The configuration space of four points on the standard CR 3-sphere up to CR-automorphisms is a real four dimensional variety as mentioned in this paper, and the existence of natural complex and CR structures on this space is proved.
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Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1
TL;DR: In this paper, generalised cross-ratios were used to prove the Ptolemaean inequality and the theorem of Ptolemius in the setting of the boundary of symmetric Riemannian spaces of rank 1 and of negative curvature.
Book ChapterDOI
Traces in complex hyperbolic geometry
TL;DR: In this article, the relationship between the geometry of complex hyperbolic manifolds and the traces of elements of the corresponding subgroup of SU(2, 1) is discussed.
References
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Volumes of hyperbolic three-manifolds
Walter D. Neumann,Don Zagier +1 more
TL;DR: In this paper, the set of all possible volumes of hyperbolic 3-manifolds is known to be a well-ordered subset of the real numbers and is of considerable interest (for number theoretic aspects see, for instance, [2], [13] and [15] ).
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Spherical hypersurfaces in complex manifolds
TL;DR: In this article, the authors make the most drastic assumption possible: they consider domains whose boundaries are everywhere locally CR equivalent to the unit sphere S 2n+l c[~n +l.