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arxiv: 1405.0025 · v1 · pith:OML2UVTHnew · submitted 2014-04-30 · 🧮 math.GT

Ptolemy coordinates, Dehn invariant, and the A-polynomial

Christian K. Zickert This is my paper
classification 🧮 math.GT
keywords a-polynomialcoordinatesdehninvariantptolemya-varietiesalgorithmboundary-unipotent
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We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2,C) A-polynomial, and more generally the SL(n,C) A-varieties. We also give a formula for the Dehn invariant of an SL(n,C)-representation.

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    Derives explicit factorization of the holonomy R-matrix for U_ξ(sl₂) at a root of unity into four geometric quantum dilogarithms satisfying a holonomy Yang-Baxter equation.