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Negatively Curved Groups Have The Convergence Property I
- ANNALES ACADEMIAE SCIENTIARUM FENNICAE
, 1995
"... It is known that the Cayley graph \Gamma of a negatively curved (Gromov-hyperbolic) group G has a well-defined boundary at infinity @ \Gamma . Furthermore, @ \Gamma is compact and metrizable. In this paper I show that G acts on @ \Gamma as a convergence group. This implies that if @ \Gamma ' S 1 ..."
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Cited by 12 (2 self)
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It is known that the Cayley graph \Gamma of a negatively curved (Gromov-hyperbolic) group G has a well-defined boundary at infinity @ \Gamma . Furthermore, @ \Gamma is compact and metrizable. In this paper I show that G acts on @ \Gamma as a convergence group. This implies that if @ \Gamma ' S 1 , then G is topologically conjugate to a cocompact Fuchsian group.
Hyperbolic geometry
- In Flavors of geometry
, 1997
"... 3. Why Call it Hyperbolic Geometry? 63 4. Understanding the One-Dimensional Case 65 ..."
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Cited by 10 (0 self)
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3. Why Call it Hyperbolic Geometry? 63 4. Understanding the One-Dimensional Case 65
Negatively Curved Groups and the Convergence Property II: Transitivity in Negatively Curved Groups
- ANNALES ACADEMIAE SCIENTIARUM FENNICAE
, 1996
"... Let G be a negatively curved group. This paper continues the classification of limit points of G that began in part I. A probability measure is constructed on the space at infinity and with respect to this measure almost every point at infinity is shown to be line transitive. ..."
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Let G be a negatively curved group. This paper continues the classification of limit points of G that began in part I. A probability measure is constructed on the space at infinity and with respect to this measure almost every point at infinity is shown to be line transitive.
