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Remarks on a conjecture of Gromov and Lawson

Geometric Topology 2018-11-28 v1 Algebraic Topology Differential Geometry K-Theory and Homology

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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Cite

@article{arxiv.math/0208011,
  title  = {Remarks on a conjecture of Gromov and Lawson},
  author = {William Dwyer and Thomas Schick and Stephan Stolz},
  journal= {arXiv preprint arXiv:math/0208011},
  year   = {2018}
}

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