A well-known property of the signature of closed oriented 4n-dimensional
manifolds is Novikov additivity, which states that if a manifold is split into
two manifolds with boundary along an oriented smooth hypersurface, then the
signature of the original manifold equals the sum of the signatures of the
resulting manifolds with boundary. Wall showed that this property is not true
of signatures on manifolds with boundary and that the difference from
additivity could be described as a certain Maslov triple index.