Remarks on a conjecture of Gromov and Lawson

Details Remarks on a conjecture of Gromov and Lawson Remarks on a conjecture of Gromov and Lawson

2002-08-02

arxiv.org/abs/math/0208011v1

High-dimensional manifold topology, Proceedings of the school held in Trieste, May 21--June 8, 2001. Edited by F. T. Farrell a

Mathematics

Geometric Topology

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Scientific paper

Gromov and Lawson conjectured that a closed spin manifold M of dimension n with fundamental group pi admits a metric with positive scalar curvature if and only if an associated element in KO_n(B pi) vanishes. In this note we present counter examples to the `if' part of this conjecture for groups pi which are torsion free and whose classifying space is a manifold with negative curvature (in the Alexandrov sense).

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