On the Hopf conjecture with symmetry

Lee Kennard

Type: Article

Publication Date: 2013-04-08

Citations: 15

DOI: https://doi.org/10.2140/gt.2013.17.563

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.

Locations

arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
Project Euclid (Cornell University) - View - PDF
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Geometry & Topology - View - PDF

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Works Cited by This (13)

Action	Title	Year	Authors
+	On Curvature and Characteristic Classes of a Riemann Manifold	1955	Shiing-shen Von Chern
+ PDF Chat	On triviality of the mod p Hopf invariant	1961	Nobuo Shimada Tsuneyo Yamanoshita
+	An exotic sphere with positive sectional curvature	2008	Peter Petersen Frederick Wilhelm
+	A 7-manifold with positive curvature	2011	Owen Dearricott
+	An Exotic $${T_{1}\mathbb{S}^4}$$ with Positive Curvature	2011	Karsten Grove Luigi Verdiani Wolfgang Ziller
+ PDF Chat	Torus actions on manifolds of positive sectional curvature	2003	Burkhard Wilking
+	THE HOPF CONJECTURE FOR MANIFOLDS WITH ABELIAN GROUP ACTIONS	2005	Xiaochun Rong Xiaole Su
+ PDF Chat	On the action of the circle group.	1957	P. E. Conner
+	The Hopf conjecture for positively curved manifolds with discrete abelian group actions	2008	Xiaole Su Yusheng Wang
+ PDF Chat	Positively curved manifolds with symmetry	2006	Burkhard Wilking