Conjecture 7 [03VE] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Conjecture 7
The homomorphism π 1 ( ℱ v ) → A u t 𝐙 P L , v ( S 2 ) \pi_{1}({\cal F}_{v})\to Aut_{{{\bf Z}}PL,v}(S^{2})
arising from the monodromy of the local system along
the leaf ℱ v {\cal F}_{v} (see Sections 3.3, 6.4) is equal
to the composition
π 1 ( ℱ v ) ↠ Γ v → A u t 𝐙 P L , v ( S 2 ) , \pi_{1}({\cal F}_{v})\twoheadrightarrow\Gamma_{v}\to Aut_{{{\bf Z}}PL,v}(S^{2})\,\,,
where the homomorphism ϕ v : Γ v → A u t 𝐙 P L , v ( S 2 ) \phi_{v}:\Gamma_{v}\to Aut_{{{\bf Z}}PL,v}(S^{2}) is
uniquely determined by this property.