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Primitive stability and Bowditch's BQ-condition are equivalent

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arxiv 1901.01396 v1 pith:NXQ44ZLB submitted 2019-01-05 math.GT

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classification math.GT
keywords primitivebowditchconditionstabilitybq-conditionconditionsdiscreteelements
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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.

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  1. On dynamics of the Mapping class group action on relative $\text{PSL}(2,\mathbb{R})$-Character Varieties

    math.GT 2025-02 conditional novelty 6.0 of 10

    Simple-stable representations of punctured surface groups into PSL(2,R) form a domain of discontinuity for the mapping class group action, and admissible hyperbolic cone surface holonomies are simple-stable, with one-...

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