Geometry & Topology
- Geom. Topol.
- Volume 17, Number 1 (2013), 563-593.
On the Hopf conjecture with symmetry
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.
Geom. Topol., Volume 17, Number 1 (2013), 563-593.
Received: 29 May 2012
Revised: 17 November 2012
Accepted: 20 December 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 55S10: Steenrod algebra
Kennard, Lee. On the Hopf conjecture with symmetry. Geom. Topol. 17 (2013), no. 1, 563--593. doi:10.2140/gt.2013.17.563. https://projecteuclid.org/euclid.gt/1513732532