On the Hopf conjecture with symmetry

Lee Kennard

doi:10.2140/gt.2013.17.563

On the Hopf conjecture with symmetry

Lee Kennard

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new tool is the action of the Steenrod algebra on cohomology.

Original language	English (US)
Pages (from-to)	563-593
Number of pages	31
Journal	Geometry and Topology
Volume	17
Issue number	1
DOIs	https://doi.org/10.2140/gt.2013.17.563
State	Published - Apr 8 2013
Externally published	Yes

Keywords

Grove program
Hopf conjecture
Positive sectional curvature
Steenrod algebra

ASJC Scopus subject areas

Geometry and Topology

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10.2140/gt.2013.17.563

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title = "On the Hopf conjecture with symmetry",

abstract = "The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new tool is the action of the Steenrod algebra on cohomology.",

keywords = "Grove program, Hopf conjecture, Positive sectional curvature, Steenrod algebra",

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AB - The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new tool is the action of the Steenrod algebra on cohomology.

KW - Grove program

KW - Hopf conjecture

KW - Positive sectional curvature

KW - Steenrod algebra

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On the Hopf conjecture with symmetry

Abstract

Keywords

ASJC Scopus subject areas

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