We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x
L(p,1), where L(p,1) is a lens space. We find that the 4d N=1,2 index on S^1 x
L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a
3d partition function on a squashed L(p,1) when the size of temporal S^1
shrinks to zero. As an application of our index, we study 4d N=2 superconformal
field theories arising from the 6d N=(2,0) A_1 theory on a punctured Riemann
surface, and conjecture the existence of a 2d Topological Quantum Field Theory
on the Riemann surface whose correlation function coincides with the 4d N=2
index on S^1 x L(p,1).Comment: 24 pages, 2 figures; v2: typos corrected, refs added, discussion of
L(p,q) remove
