Bases for cluster algebras from surfaces

We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, for example, principal coefficients.Comment: 53 pages; v2 references update

Co-contractions of Graphs and Right-angled Artin Groups

We define an operation on finite graphs, called co-contraction. By showing that co-contraction of a graph induces an injective map between right-angled Artin groups, we exhibit a family of graphs, without any induced cycle of length at least 5, such that the right-angled Artin groups on those graphs contain hyperbolic surface groups. This gives the negative answer to a question raised by Gordon, Long and Reid.Comment: 18 pages, 8 figure