Mathematics – Rings and Algebras
Scientific paper
2006-08-15
Acta Mathematica, 201:83-146, 2008
Mathematics
Rings and Algebras
56 pages, 32 figures. Revised in response to referee comments
Scientific paper
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.
Fomin Sergey
Shapiro Michael
Thurston Dylan
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