The primitive-stable domain conjecture for free-group character varieties

Let FnF_n be the free group of rank nn, let X(Fn){\mathcal X}(F_n) be its PSL2(C){\operatorname{PSL}_2(\mathbb C)} character variety, and let PS(Fn){\mathcal{PS}}(F_n) denote the primitive-stable locus. Primitive-stable domain conjecture. The domain of discontinuity PS(Fn){\mathcal{PS}}(F_n) is the domain of discontinuity of Out(Fn)Out(F_n) acting on X(Fn){\mathcal X}(F_n). The claim concerns whether the primitive-stable locus gives the full properly discontinuous domain for the Out(Fn)Out(F_n) action; the source presents this as a conjectural implication and does not state a resolution.

Sources & referencesView supporting material

Primary source

Yair N. Minsky, “On dynamics of Out(F_n) on PSL(2,C) characters”, arXiv:0906.3491 (2010).

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