@article{60630845c476419d81f1b66382e2c7fb,
title = "On a generalized conjecture of Hopf with symmetry",
abstract = "A famous conjecture of Hopf states that does not admit a Riemannian metric with positive sectional curvature. In this article, we prove that no manifold product can carry a metric of positive sectional curvature admitting a certain degree of torus symmetry.",
keywords = "Euler characteristic, Hopf conjecture, positive curvature, torus symmetry",
author = "Manuel Amann and Lee Kennard",
note = "Funding Information: We would like to thank B. Wilking for a motivating discussion on calculating Euler characteristics of positively curved manifolds with symmetry. We are also grateful to W. Ziller for alerting us to Asoh's paper. The first author was supported by a research grant of the German Research Foundation. The second author was supported by National Science Foundation grants DMS-1045292 and DMS-1404670. Publisher Copyright: {\textcopyright} 2017 The Authors.",
year = "2017",
month = feb,
day = "1",
doi = "10.1112/S0010437X16008150",
language = "English (US)",
volume = "153",
pages = "313--322",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "2",
}