On the Hopf Conjecture with Symmetry

Details On the Hopf Conjecture with Symmetry On the Hopf Conjecture with Symmetry

2012-03-16

arxiv.org/abs/1203.3808v1

Mathematics

Differential Geometry

Scientific paper

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.

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