• Corpus ID: 233219655

The mutation compatibility of the ${\rm SL}_3$ quantum trace maps for surfaces

@inproceedings{Kim2021TheMC,
  title={The mutation compatibility of the \$\{\rm SL\}\_3\$ quantum trace maps for surfaces},
  author={Hyun Kyu Kim},
  year={2021}
}
Fock-Goncharov’s moduli spaces XPGL3,S of framed PGL3-local systems on punctured surfaces S provide prominent examples of cluster X -varieties and higher Teichmüller spaces. In a previous paper of the author (arXiv:2011.14765), the so-called SL3 quantum trace map is constructed for each triangulable punctured surface S and its ideal triangulation ∆, as a homomorphism from the stated SL3-skein algebra of the surface to a quantum torus algebra that deforms the ring of Laurent polynomials in the… 

Figures from this paper

Quantum traces for $\mathrm{SL}_n(\mathbb{C})$: the case $n=3$.
We generalize Bonahon and Wong's $\mathrm{SL}_2(\mathbb{C})$-quantum trace map to the setting of $\mathrm{SL}_3(\mathbb{C})$. More precisely, for each non-zero complex number $q$, we associate to

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