Cluster algebras and triangulated surfaces. Part I: Cluster complexes

Details Cluster algebras and triangulated surfaces. Part I: Cluster complexes Cluster algebras and triangulated surfaces. Part I: Cluster complexes

2006-08-15

arxiv.org/abs/math/0608367v3

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.

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