Abstract
We generalize Bonahon–Wong's SL2(C)-quantum trace map to the setting of SL3(C). More precisely, given a non-zero complex parameter q=e2πiħ, we associate to each isotopy class of framed oriented links K in a thickened punctured surface S×(0,1) a Laurent polynomial Trλq(K)=Trλq(K)(Xiq) in q-deformations Xiq of the Fock–Goncharov X-coordinates for higher Teichmüller space. This construction depends on a choice λ of ideal triangulation of the surface S. Along the way, we propose a definition for a SLn(C)-version of this invariant.
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