We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of coefficients, describe this complex explicitly in terms of tagged triangulations of the surface, and determine its homotopy type and its growth rate.
No takes yet. Share an insight, caveat, or question.
Fomin et al. (2008) studied this question.
Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context: