Topological interference alignment refers to the alignment of interference in
partially connected linear communication networks, wired and wireless, when
only
the knowledge of the end-to-end network topology is available to the
transmitters. In particular the values of the non-zero channel coefficients
are
not known to the transmitters. We show that in general with arbitrary
connectivity, the capacity of the wired network, and the degrees of freedom of
the corresponding wireless network, are intimately connected to a
corresponding
index coding problem, and interference alignment plays a non-trivial role in
the
solution of all three problems.