Math @ Duke

Publications [#337147] of Shira Viel
Papers Published
 Barnard, E; Meehan, E; Reading, N; Viel, S, Universal Geometric Coefficients for the FourPunctured Sphere,
Annals of Combinatorics, vol. 22 no. 1
(March, 2018),
pp. 144, Springer Nature [doi]
(last updated on 2021/05/12)
Abstract: We construct universal geometric coefficients for the cluster algebra associated to the fourpunctured sphere and obtain, as a byproduct, the gvectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasilaminations). The classification allows us to prove the Null Tangle Property for the fourpunctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute shear coordinates explicitly to obtain universal geometric coefficients.


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