2006/08/31 by Sergey Fomin, Michael Shapiro, Dylan Thurston · 1 citation
Mathematics · #math.CO #math.GT #math.RA #msc:16S99 #msc:57M50 #msc:57N05
published as Acta Mathematica, 201:83-146, 2008 · 56 pages, 32 figures. Revised in response to referee comments
arxiv created 2007/08/20 · arxiv updated 2010/03/15
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.