Primitive stability and the Bowditch conditions revisited

2020/06/18 by Series, Caroline · 2 citations
#30F40 (primary) #57M50 (secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2006.10403

Abstract

The equivalence of two conditions on the primitive elements in an SL(2,\mathbb C) representation of the free group F₂ = , namely Minsky's condition of primitive stability and the BQ-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.

Cited by

• Bowditch representations in Gromov-hyperbolic spaces : characterizations, dynamics of Out(\mathbbF₂) and recognition
• Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space

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