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arXiv · 1203.3808

On the Hopf Conjecture with Symmetry

Lee Kennard
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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.

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Lee Kennard. 2012-03-16. On the Hopf Conjecture with Symmetry. https://doi.org/10.2140/gt.2013.17.563

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