ScalingStacks

Conjecture 7 [03VE]

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Conjecture 7

The homomorphism π1​(ℱv)→A​u​t𝐙​P​L,v​(S2)\pi_{1}({\cal F}_{v})\to Aut_{{{\bf Z}}PL,v}(S^{2}) arising from the monodromy of the local system along the leaf ℱv{\cal F}_{v} (see Sections 3.3, 6.4) is equal to the composition

π1​(ℱv)↠Γv→A​u​t𝐙​P​L,v​(S2),\pi_{1}({\cal F}_{v})\twoheadrightarrow\Gamma_{v}\to Aut_{{{\bf Z}}PL,v}(S^{2})\,\,,

where the homomorphism ϕv:Γv→A​u​t𝐙​P​L,v​(S2)\phi_{v}:\Gamma_{v}\to Aut_{{{\bf Z}}PL,v}(S^{2}) is uniquely determined by this property.

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