Universality of actions on $\mathbb HP^2$

Abstract

We show that any eight-dimensional oriented manifold $M$ possessing smooth circle action with exactly three fixed points has the same weight system as some circle action on $\mathbb HP^2$. It follows that Pontryagin numbers and equivariant cohomology of $M$ coincide to that of $\mathbb HP^2$; if $M$ admits cellular decomposition of only three cells, it is diffeomorphic to $\mathbb HP^2$.