A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
Thomas Schick
Abstract
Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with π1(M) = Z4times Z/3, so that the index invariant in the KO-theory of the reduced C*-algebra of π1(M) is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov-Lawson-Rosenberg conjecture.
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