Cluster algebras and triangulated surfaces. Part I: Cluster complexes

Abstract

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.

56 pages, 32 figures. Revised in response to referee comments

References in corpus (4)

• Semicanonical bases and preprojective algebras
• Cluster ensembles, quantization and the dilogarithm
• Probing mapping class groups using arcs
• The Structure and Singularities of Arc Complexes

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