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Remarks on a conjecture of Gromov and Lawson

William Dwyer, Thomas Schick, Stephan Stolz

Published 2002-08-02Version 1

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).

Comments: LaTeX2e, 14 pagers
Journal: High-dimensional manifold topology, Proceedings of the school held in Trieste, May 21--June 8, 2001. Edited by F. T. Farrell and W. L\~A1/4ck. 159--176, World Sci. Publ., River Edge, NJ, 2003.
Categories: math.GT, math.AT, math.DG, math.KT
Subjects: 53C21
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