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.