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      A classification of radial or totally geodesic ends of real projective orbifolds I: a survey of results

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          Abstract

          Real projective structures on \(n\)-orbifolds are useful in understanding the space of representations of discrete groups into \(\mathrm{SL}(n+1, \mathbb{R})\) or \(\mathrm{PGL}(n+1, \mathbb{R})\). A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the original ones. The purpose of this paper is to understand the structures of ends of real projective \(n\)-dimensional orbifolds. In particular, these have the radial or totally geodesic ends. Hyperbolic manifolds with cusps and hyper-ideal ends are examples. For this, we will study the natural conditions on eigenvalues of holonomy representations of ends when these ends are manageably understandable. We will show that only the radial or totally geodesic ends of lens type or horospherical ends exist for strongly irreducible properly convex real projective orbifolds under the suitable conditions. The purpose of this article is to announce these results.

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          Author and article information

          Journal
          2015-01-02
          2016-01-26
          Article
          1501.00348
          4a835c7f-1241-442d-ac16-d4e35b8e75a5

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          57M50, 53A20, 53C15
          53 pages, 4 figures. This paper surveys the results in the paper "The classification of radial and totally geodesic ends of properly convex real projective orbifolds" arXiv:1304.1605, which will be divided into three papers, one of which is this one. Some errors of the previous version are corrected
          math.GT

          Geometry & Topology
          Geometry & Topology

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