On the hopf conjecture with symmetry

Research output: Chapter in Book/Entry/PoemChapter


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


Dive into the research topics of 'On the hopf conjecture with symmetry'. Together they form a unique fingerprint.

Cite this