  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. Perverse
signatures are signatures defined for any stratified pseudomanifold, using the
intersection homology groups of Goresky and MacPherson. In the case of Witt
spaces, the middle perverse signature is the same as the Witt signature. This
paper proves a generalization to perverse signatures of Wall's non-additivity
theorem for signatures of manifolds with boundary. Under certain topological
conditions on the dividing hypersurface,Novikov additivity for perverse
signatures may be deduced as a corollary. In particular, Siegel's version of
Novikov additivity for Witt signatures is a special case of this corollary.
