The Gromov–Lawson–Rosenberg conjecture predicts which high-dimensional Spin manifolds admit a metric of positive scalar curvature (psc). A priori this is a purely differential geometric problem which begs the question why topologists care about it. The answer is that positive scalar curvature has two great links to topology. The first comes from index theory. If \((M,g)\) carries a spin structure, there exists a so called Dirac operator on \(M\) whose index is an obstruction to the existence of a psc metric. The second one is the Gromov-Lawson surgery theorem which states that the existence of a psc metric is invariant under high codimension surgery. These two results interact nicely, which allows one to prove the above named conjecture for simply connected manifolds of dimension at least 5.