  The superconformal index of the quiver gauge theory dual to type IIB string
theory on the product of an arbitrary smooth Sasaki-Einstein manifold with
five-dimensional AdS space is calculated both from the gauge theory and gravity
viewpoints. We find complete agreement. Along the way, we find that the index
on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of
the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals
the Euler characteristic of the cyclic homology of the Ginzburg dg algebra
associated to the quiver.
