On the Hopf conjectures with symmetry

Lee Kennard, University of Pennsylvania

Abstract

We prove results related to the classical Hopf conjectures about positively curved manifolds under the assumption of a logarithmic symmetry rank bound. The main new tool is the action of the Steenrod algebra on cohomology. Along the way, we formulate a certain notion of periodicity in cohomology and obtain a generalization in this context of Adem's theorem on singly generated cohomology rings.^

Subject Area

Applied Mathematics|Mathematics

Recommended Citation

Lee Kennard, "On the Hopf conjectures with symmetry" (January 1, 2012). Dissertations available from ProQuest. Paper AAI3509156.
http://repository.upenn.edu/dissertations/AAI3509156

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