  String structures in degree four are associated with cancellation of
anomalies of string theory in ten dimensions. Fivebrane structures in degree
eight have recently been shown to be associated with cancellation of anomalies
associated to the NS5-brane in string theory as well as the M5-brane in
M-theory. We introduce and describe "Ninebrane structures" in degree twelve and
demonstrate how they capture some anomaly cancellation phenomena in M-theory.
Along the way we also define certain variants, considered as intermediate cases
in degree nine and ten, which we call "2-Orientation" and "2-Spin structures",
respectively. As in the lower degree cases, we also discuss the natural twists
of these structures and characterize the corresponding topological groups
associated to each of the structures, which likewise admit refinements to
differential cohomology.
