  We give a geometric model for a tube category in terms of homotopy classes of
oriented arcs in an annulus with marked points on its boundary. In particular,
we interpret the dimensions of extension groups of degree 1 between
indecomposable objects in terms of negative geometric intersection numbers
between corresponding arcs, giving a geometric interpretation of the
description of an extension group in the cluster category of a tube as a
symmetrized version of the extension group in the tube. We show that a similar
result holds for finite dimensional representations of the linearly oriented
quiver of type A-double-infinity.
