Cluster algebras and triangulated surfaces. Part I: Cluster complexes
نویسندگان
چکیده
منابع مشابه
A ug 2 00 6 CLUSTER ALGEBRAS AND TRIANGULATED SURFACES PART I : CLUSTER COMPLEXES
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.
متن کامل0 A ug 2 00 7 CLUSTER ALGEBRAS AND TRIANGULATED SURFACES PART I : CLUSTER COMPLEXES
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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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.
متن کاملCluster Algebras and Triangulated Surfaces Part Ii: Lambda Lengths
We construct geometric models for cluster algebras associated with bordered surfaces with marked points, for any choice of coefficients of geometric type, using generalized decorated Teichmüller spaces. In this context, the cluster variables are interpreted as suitably renormalized lambda lengths.
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These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2008
ISSN: 0001-5962
DOI: 10.1007/s11511-008-0030-7