Maps on Boundaries of Hyperbolic Metric SpacesUniversity of California, Berkeley, 1997 - 132 pages |
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0)-quasi-isometric section 3-manifold 8-hyperbolic A₂ Ã Andrew Casson assume automorphism bi-infinite geodesic C₁ C₂ Cannon-Thurston map Cayley graph Chabauty topology Choosing conjugacy class construct contained continuous map converging Corollary coset cyclic conjugate define denote a geodesic distortion function do(x e)-quasigeodesics edge edge-path representative ending laminations exact sequence exists ƏÃQ finitely generated groups following Lemma free homotopy representative geodesic joining geodesic path geodesic ray geodesic representative geodesic segment geodesic subsegment H-invariant H₁ Hence homeomorphic hyperbolic 3-manifold hyperbolic group hyperbolic metric spaces hyperbolic subgroup identity injectivity radius injn(x joining the end-points K₁ depends Kleinian groups leaf Lemma Let H lies main theorem metric spaces satisfying neighborhood normal subgroup path metric pleated surfaces Proof Proposition 3.1.1 quasi-isometrically embedded quasiconvex quasigeodesic r₁ Recall short exact sequence shortest single-valued quasi-isometric section subset T₁ Teichmuller Thurston map vertex set vertices Y₁ гн