Limits of conjugacy classes under iterates of hyperbolic elements of Out()

  • Pritam Ghosh

    Ashoka University, Sonipat, India
Limits of conjugacy classes under iterates of hyperbolic elements of Out($\mathbb F$) cover

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Abstract

For a free group of finite rank such that rank , we prove that the set of weak limits of a conjugacy class in under iterates of some hyperbolic is equal to the collection of generic leaves and lines with endpoints in attracting fixed points of .

As an application we describe the ending lamination set for a hyperbolic extension of by a hyperbolic element of Out() in a new way and use it to prove results about Cannon–Thurston maps for such extensions. We also use it to derive conditions for quasiconvexity of finitely generated, infinite index subgroups of in the extension group. These results generalize similar results obtained in [23] and [19] and use different techniques.

Cite this article

Pritam Ghosh, Limits of conjugacy classes under iterates of hyperbolic elements of Out(). Groups Geom. Dyn. 14 (2020), no. 1, pp. 177–211

DOI 10.4171/GGD/540