On the hopf conjecture with symmetry

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationGeometry of Manifolds with Non-Negative Sectional Curvature
Subtitle of host publicationEditors: Rafael Herrera, Luis Hernandez-Lamoneda
PublisherSpringer Verlag
Number of pages6
ISBN (Print)9783319063720
StatePublished - 2014
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Kennard, L. (2014). On the hopf conjecture with symmetry. In Geometry of Manifolds with Non-Negative Sectional Curvature: Editors: Rafael Herrera, Luis Hernandez-Lamoneda (pp. 111-116). (Lecture Notes in Mathematics; Vol. 2110). Springer Verlag. https://doi.org/10.1007/978-3-319-06373-7_5