A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture

Details A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture

2004-03-03

arxiv.org/abs/math/0403063v1

Topology 37, 1165-1168 (1998)

Mathematics

Geometric Topology

4 pages, old

Scientific paper

Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with $\pi_1(M) = Z^4times Z/3$, so that the index invariant in the KO-theory of the reduced $C^*$-algebra of $\pi_1(M)$ 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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