Geometric model for tube categories

Joint work with Robert Marsh (Leeds)

We describe how to construct tube categories using arcs (up to homotopy) in an annulus

with marked points on the boundary. This allows us to compute the dimension of Ext^1

between two indecomposable objects: It corresponds to the (signed) crossing number of the

corresponding arcs. As a consequence, we also get the dimension of Ext^1 in the cluster tube

as a symmetric version of this.