67 citations · 136 across the 4 of their papers we have counts for
4 papers
Cluster X-varieties at infinity
V. V. Fock, A. B. Goncharov
A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a…
Cluster ensembles, quantization and the dilogarithm II: The intertwiner
V. V. Fock, A. B. Goncharov
The main result is a construction, via the quantum dilogarithm, of certain intertwiner operators, which play the crucial role in the quantization of the cluster X-varieties and con…
Dual Teichmuller and lamination spaces
V. V. Fock, A. B. Goncharov
We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfa…
Cluster ensembles, quantization and the dilogarithm
V. V. Fock, A. B. Goncharov
Cluster ensemble is a pair of positive spaces (X, A) related by a map p: A -> X. It generalizes cluster algebras of Fomin and Zelevinsky, which are related to the A-space. We devel…