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).
Keywords
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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