Primitive stability and the Bowditch conditions revisited

preprint2020arXivOpen access

Abstract

The equivalence of two conditions on the primitive elements in an SL(2,C)SL(2,\mathbb C) representation of the free group F2=<a,b>F_2 = <a,b>, namely Minsky's condition of primitive stability and the BQBQ-conditions introduced by Bowditch and generalised by Tan, Wong and Zhang, has been proved by Lee and Xu and independently by the author in arXiv:1901.01396. This note is a revised version of our original proof, which is greatly simplified by incorporating some of the ideas introduced by Lee and Xu, combined with the language of the Bowditch tree.

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