Ninebrane structures

String structures in degree 4 are associated with cancelation of anomalies of string theory in 10 dimensions. Fivebrane structures in degree 8 have recently been shown to be associated with cancelation of anomalies associated to fivebranes in string theory and M-theory. We introduce and describe Ninebrane structures in degree 12 and demonstrate how they capture some anomaly cancelation phenomena in M-theory. Along the way we also define certain variants, considered as intermediate cases in degrees 9 and 10, 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.