Remarks on a conjecture of Gromov and Lawson

William Dwyer; Thomas Schick; Stephan Stolz

doi:10.1142/9789812704443_0008

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Remarks on a conjecture of Gromov and Lawson

William Dwyer·Thomas Schick·Stephan Stolz

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Abstract

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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William Dwyer, Thomas Schick, Stephan Stolz. 2002-08-02. Remarks on a conjecture of Gromov and Lawson. https://doi.org/10.1142/9789812704443_0008

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