On the Hopf conjectures with symmetry
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.^
Kennard, Lee, "On the Hopf conjectures with symmetry" (2012). Dissertations available from ProQuest. AAI3509156.