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

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

2009-10-12

arxiv.org/abs/0910.2114v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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