  The surgery technique of Gromov and Lawson may be used to construct families
of positive scalar curvature metrics which are parameterised by Morse
functions. This has played an important role in the study of the space of
metrics of positive scalar curvature on a smooth manifold and its corresponding
moduli spaces. In this paper, we extend this technique to work for families of
generalised Morse functions, i.e. smooth functions with both Morse and
birth-death singularities.
