Relative Hyperbolicity , Trees of Spaces And
نویسنده
چکیده
We prove the existence of continuous boundary extensions (Cannon-Thurston maps) for the inclusion of a vertex space into a tree of (strongly) relatively hyperbolic spaces satisfying the qi-embedded condition. This implies the same result for inclusion of vertex (or edge) subgroups in finite graphs of (strongly) relatively hyperbolic groups. This generalises a result of Bowditch for punctured surfaces in 3 manifolds and a result of Mitra for trees of hyperbolic metric spaces.
منابع مشابه
N ov 2 00 6 A Combination Theorem for Strong Relative Hyperbolicity Mahan
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups.
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We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn’s Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Combination Theorem. AMS subject classification = 20F32(Primary), 57M50(Secondary)
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We prove the existence of continuous boundary extensions (Cannon-Thurston maps) for the inclusion of a vertex space into a tree of (strongly) relatively hyperbolic spaces. The result follows for finite graphs of (strongly) relatively hyperbolic groups. This generalises a result of Bowditch for punctured surfaces in 3 manifolds. AMS subject classification = 20F32(Primary), 57M50(Secondary)
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