  The topological part of the M-theory partition function was shown by Witten
to be encoded in the index of an E8 bundle in eleven dimensions. This partition
function is, however, not automatically anomaly-free. We observe here that the
vanishing W_7=0 of the Diaconescu-Moore-Witten anomaly in IIA and compactified
M-theory partition function is equivalent to orientability of spacetime with
respect to (complex-oriented) elliptic cohomology. Motivated by this, we define
an elliptic cohomology correction to the IIA partition function, and propose
its relationship to interaction between 2-branes and 5-branes in the M-theory
limit.
