Asymptotic windings of horocycles |
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Authors: | Dmitry Dolgopyat Omri Sarig |
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Institution: | 1.Department of Mathematics, Statistics, and Computer Science,University of Illinois at Chicago,Chicago,USA;2.Centre for Mathematical Sciences,DPMMS,Cambridge,UK |
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Abstract: | Let Γ be a torsion-free hyperbolic group. We study Γ-limit groups which, unlike the fundamental case in which Γ is free, may not be finitely presentable or geometrically tractable. We define model Γ-limit groups, which always have good geometric properties (in particular, they are always relatively hyperbolic). Given a strict resolution of an arbitrary Γ-limit group L, we canonically construct a strict resolution of a model Γ-limit group, which encodes all homomorphisms L → Γ that factor through the given resolution. We propose this as the correct framework in which to study Γ-limit groups algorithmically. We enumerate all Γ-limit groups in this framework. |
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