Metrics of positive scalar curvature and connections with surgery (Q2708390)

This article surveys the connection between the existence and uniqueness of Riemannian metrics of positive scalar curvature on a manifold and the topology of the manifold. Developments of the past 25 years are outlined, sketches of the proofs of some of the main results are given, and some open problems are discussed. Three main topics are covered. The first is the Surgery Theorem of Gromov-Lawson and Schoen-Yau asserting that surgery of codimension greater than two on a closed manifold with a positive scalar curvature metric results in another manifold with a positive scalar curvature metric. The second is the Gromov-Lawson Conjecture, which relates the existence of positive scalar curvature metrics to index theory and \(KO\)-homology. The third is that approach, due mainly to the second author, to the study of positive scalar curvature metrics, which parallels Wall's surgery theoretic classification of manifolds.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00062].