Metrics of positive scalar curvature and generalised Morse functions, part II

Abstract

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.Comment: 49 pages, 36 figures. This is a substantial revision of the previous version, containing a number of new result