Metrics of positive scalar curvature and generalised Morse functions, part 1

Details Metrics of positive scalar curvature and generalised Morse functions, part 1 Metrics of positive scalar curvature and generalised Morse functions, part 1

2008-11-08

arxiv.org/abs/0811.1245v1

Mathematics

Differential Geometry

81 pages, 61 figures

Scientific paper

It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. We show that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.

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