Conical limit sets of hyperbolic subgroups

2013/01/15 by Woojin Jeon, Jeon, Woojin, Ken'ichi Ohshika +1
Mathematics · #20F67 #51M10 #57S25 #60J50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F67 #msc:51M10 #msc:57S25 #msc:60J50

paper · pdf · doi:10.48550/arxiv.1301.3229

This paper has been withdrawn by the author due to a gap in the proof of the main Theorem

arxiv created 2013/08/22 · arxiv updated 2013/08/23

Abstract

Given a hyperbolic subgroup H of a hyperbolic group G for which a Cannon-Thurston map i:∂ H \ra ∂ G exists, we study the limit set Λ_H of H with respect to its action on ∂ G. We prove that the set of conical limit points is exactly the subset of Λ_H consisting of the points to which the Cannon-Thurston map i injects. Moreover, we show that when H is not quasi-convex in G, there exists a non-conical limit point in Λ_H

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