  This paper addresses the following question: given a topological quantum
field theory on $\mathbb R^n$ built from an action functional, when is it
possible to globalize the theory so that it makes sense on an arbitrary smooth
oriented $n$-manifold? We study a broad class of topological field theories --
those of AKSZ type -- and obtain an explicit condition for the vanishing of the
framing anomaly, i.e., the obstruction to performing this globalization
procedure. We also interpret our results in terms of identifying the
observables as an algebra over the framed little $n$-disks operad. Our analysis
uses the BV formalism for perturbative field theory and the notion of
factorization homology.
