Titel: On some recent results concerning the Gromov-Lawson-Rosenberg Conjecture for finite groups
The Gromov-Lawson-Rosenberg Conjecture states that a closed connected spin manifold of dimension $n$ greater or equal to 5 with fundamental group $\pi$ admits a Riemannian metric with positive scalar curvature if and only if a certain index theoretically constructed obstruction class in the $n$-th $K$-theory group of the reduced group $C^*$-algebra $C^*_r\pi$ vanishes. Although the general conjecture has been disproved (by Schick) it makes sense to ask wether or not the conjecture is true for specific fundamental groups. So far no counterexample with a finite fundamental group has been found. In our talk we will report on recent results concerning the Gromov-Lawson-Rosenberg Conjecture for manifolds with finite fundamental group.