Cluster algebras and triangulated surfaces. Part I: Cluster complexes
Rings and Algebras
2010-03-15 v3 Combinatorics
Geometric Topology
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.
Cite
@article{arxiv.math/0608367,
title = {Cluster algebras and triangulated surfaces. Part I: Cluster complexes},
author = {Sergey Fomin and Michael Shapiro and Dylan Thurston},
journal= {arXiv preprint arXiv:math/0608367},
year = {2010}
}
Comments
56 pages, 32 figures. Revised in response to referee comments