Abstract
The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new tool is the action of the Steenrod algebra on cohomology.
Citation
Lee Kennard. "On the Hopf conjecture with symmetry." Geom. Topol. 17 (1) 563 - 593, 2013. https://doi.org/10.2140/gt.2013.17.563
Information