Metrics of positive scalar curvature on spheres and the Gromov-Lawson conjecture (Q1105204)

Call two metrics \(g_ 0\) and \(g_ 1\) of positive scalar curvature on a closed manifold M concordant if there is a metric g on \(M\times [0,1]\) of positive scalar curvature such that \(g| M\times \{i\}=g_ i\) and g is a product near \(\partial (M\times [0,1])\). If X is 2-connected and closed, B an n-ball in X, then by the results of Gromov-Lawson and Schoen-Yau, there is a metric of positive scalar curvature on \(X\setminus B\) which is a product near \(S^{n-1}=\partial (X\setminus Int B).\) The author shows that the concordance class of the resulting metric on \(S^{n-1}\) depends only on the spin cobordism class of X and furthermore discusses related questions.