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arXiv · 1901.04166

Cluster structures and subfans in scattering diagrams

Yan Zhou
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Abstract

We give more precise statements of Fock-Goncharov duality conjecture for cluster varieties parametrizing ${\rm SL}_{2}/{\rm PGL}_{2}$-local systems on the once punctured torus. Then we prove these statements. Along the way, using distinct subfans in the scattering diagram, we produce an example of a cluster variety with two non-equivalent cluster structures. To overcome the technical difficulty of infinite non-cluster wall-crossing in the scattering diagram, we introduce quiver folding into the machinery of scattering diagrams and give a quotient construction of scattering diagrams.

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Yan Zhou. 2019-01-14. Cluster structures and subfans in scattering diagrams. https://doi.org/10.3842/sigma.2020.013

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