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. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Kennard, L. (2014). On the hopf conjecture with symmetry. Lecture Notes in Mathematics, 2110, 111–116. https://doi.org/10.1007/978-3-319-06373-7_5
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