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.
| Original language | English (US) |
|---|---|
| Title of host publication | Geometry of Manifolds with Non-Negative Sectional Curvature |
| Subtitle of host publication | Editors: Rafael Herrera, Luis Hernandez-Lamoneda |
| Publisher | Springer Verlag |
| Pages | 111-116 |
| Number of pages | 6 |
| ISBN (Print) | 9783319063720 |
| DOIs | |
| State | Published - 2014 |
| Externally published | Yes |
Publication series
| Name | Lecture Notes in Mathematics |
|---|---|
| Volume | 2110 |
| 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