Relatively hyperbolic extensions of groups and Cannon-Thurston maps |
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Authors: | Abhijit Pal |
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Institution: | 1.Stat-Math Unit,Indian Statistical Institute,Kolkata,India |
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Abstract: | Let 1 → (K, K
1) → (G, N
G
(K
1)) → (Q, Q
1) → 1 be a short exact sequence of pairs of finitely generated groups with K
1 a proper non-trivial subgroup of K and K strongly hyperbolic relative to K
1. Assuming that, for all g ∈ G, there exists k
g
∈ K such that gK
1
g
−1 = k
g
K
1
k
g−1, we will prove that there exists a quasi-isometric section s: Q → G. Further, we will prove that if G is strongly hyperbolic relative to the normalizer subgroup N
G
(K
1) and weakly hyperbolic relative to K
1, then there exists a Cannon-Thurston map for the inclusion i: Γ
K
→ Γ
G
. |
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Keywords: | |
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