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On the Hopf Conjecture with Symmetry

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Geometry of Manifolds with Non-negative Sectional Curvature

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2110))

Abstract

The Hopf conjecture states that an even-dimensional manifold with positive curvature has positive Euler characteristic. We show that this is true under the assumption that a torus of sufficiently large dimension acts by isometries. This improves previous results by replacing linear bounds by a logarithmic bound. The new method that is introduced is the use of Steenrod squares combined with geometric arguments of a similar type to what was done before.

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Authors and Affiliations

  1. Department of Mathematics, University of California, South Hall, Room 6607, Santa Barbara, CA, 93106-3080, USA

    Lee Kennard

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  1. Lee Kennard
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Kennard, L. (2014). On the Hopf Conjecture with Symmetry. In: Geometry of Manifolds with Non-negative Sectional Curvature. Lecture Notes in Mathematics, vol 2110. Springer, Cham. https://doi.org/10.1007/978-3-319-06373-7_5

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