  A once-extended d-dimensional topological field theory Z is a symmetric
monoidal functor (taking values in a chosen target symmetric monoidal
(infty,2)-category) assigning values to (d-2)-manifolds, (d-1)-manifolds, and
d-manifolds. We show that if Z is at least once-extended and the value assigned
to the (d-1)-torus is invertible, then the entire topological field theory is
invertible, that is it factors through the maximal Picard infty-category of the
target. Results are obtained in the presence of arbitrary tangential
structures.
