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

2008/11/08 by Mark Walsh, Walsh, Mark · 1 citation
Mathematics · #53C20 #58J53 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0811.1245

openalex publication_date 2008/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Morse theory and higher torsion invariants II

Cited by

• Highly connected manifolds of positive p-curvature

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