On the hopf conjecture with symmetry

Lee Kennard

doi:10.1007/978-3-319-06373-7_5

On the hopf conjecture with symmetry

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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	https://doi.org/10.1007/978-3-319-06373-7_5
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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10.1007/978-3-319-06373-7_5

Cite this

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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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On the hopf conjecture with symmetry

Abstract

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