  We show that general N=2 supersymmetric AdS_4 solutions of M-theory with
non-zero M2-brane charge admit a canonical contact structure. The free energy
of the dual superconformal field theory on S^3 and the scaling dimensions of
operators dual to supersymmetric wrapped M5-branes are expressed via AdS/CFT in
terms of contact volumes. In particular, this leads to topological and
localization formulae for the coefficient of N^{3/2} in the free energy of such
solutions.
