A Counterexample to a Conjecture about Positive Scalar Curvature
Geometric Topology
2015-07-16 v4 Algebraic Topology
K-Theory and Homology
Abstract
Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in Schick: "A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture".
Keywords
Cite
@article{arxiv.1102.2916,
title = {A Counterexample to a Conjecture about Positive Scalar Curvature},
author = {Daniel Pape and Thomas Schick},
journal= {arXiv preprint arXiv:1102.2916},
year = {2015}
}
Comments
v1: 4 pages, AMS-LaTeX; v2: small changes in presentation, typos corrected, v3: comment added, to appear in Proc AMS