Primitive stability and Bowditch's BQ-condition are equivalent

Abstract

We prove the equivalence of two conditions on the primitive elements in an $SL(2,\mathbb{C})$ representation of the free group $F_2$ on two generators, which may hold even when the image of $F_2$ is not discrete. One is Minsky's condition of primitive stability and the other is the $BQ$-condition introduced by Bowditch and generalised by Tan, Wong and Zhang.

20 pages, 2 figures

References in corpus (2)

• The Modular Group Action on Real SL(2)-characters of a One-Holed Torus
• Generalized Markoff Maps and McShane's Identity

Cited by in corpus (2)

• Bowditch's Q-conditions and Minsky's primitive stability
• Weakly positive and directed Anosov representations