A duality map for quantum cluster varieties from surfaces

Dylan G.L. Allegretti, Hyun Kyu Kim

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the “quantum trace” map introduced by Bonahon and Wong.

Original languageEnglish
Pages (from-to)1164-1208
Number of pages45
JournalAdvances in Mathematics
StatePublished - 14 Jan 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Canonical basis
  • Cluster variety
  • Quantization
  • Skein algebra


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