arXiv 1506.080362015-06math.GTmath.GR

Algebraic Ending Laminations and Quasiconvexity

Mahan Mj, Kasra Rafi

备注：: Final version incorporating referee comments. 26 pgs 1 fig
发表信息：: Algebr. Geom. Topol. 18 (2018) 1883-1916
DOI：: 10.2140/agt.2018.18.1883

英文摘要：

We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence $$1\to H\to G \to Q \to 1 $$ of hyperbolic groups. These laminations arise in different contexts: existence of Cannon-Thurston maps; closed geodesics exiting ends of manifolds; dual to actions on $\R-$trees. We use the relationship between these laminations to prove quasiconvexity results for finitely generated infinite index subgroups of $H$, the normal subgroup in the exact sequence above.

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