English

Primitive stability and the Bowditch conditions revisited

Geometric Topology 2020-06-19 v1

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.

Cite

@article{arxiv.2006.10403,
  title  = {Primitive stability and the Bowditch conditions revisited},
  author = {Caroline Series},
  journal= {arXiv preprint arXiv:2006.10403},
  year   = {2020}
}

Comments

20 pages , 3 figures. This paper is a substantial revision and simplification of arXiv:1901.01396

R2 v1 2026-06-23T16:25:40.893Z