  We show that the non-critical $c=1$ string at the self-dual radius is
equivalent to topological strings based on the deformation of the conifold
singularity of Calabi-Yau threefolds. The Penner sum giving the genus expansion
of the free energy of the $c=1$ string theory at the self-dual radius therefore
gives the universal behaviour of the topological partition function of a
Calabi-Yau threefold near a conifold point.
