On the Hopf conjecture with symmetry

Kennard, Lee¹

¹ Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106-3080, USA

Geometry & topology, Tome 17 (2013) no. 1, pp. 563-593.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.563

Classification : 53C20, 55S10
Keywords: positive sectional curvature, Hopf conjecture, Grove program, Steenrod algebra

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