Universality of actions on $\mathbb{H}{P}^2$

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 $\mathbb{H}{P}^2$. It follows that Pontryagin numbers and equivariant cohomology of $M$ coincide to that of $\mathbb{H}{P}^2$; if $M$ admits cellular decomposition of only three cells, it is diffeomorphic to $\mathbb{H}{P}^2$.

References in corpus (1)

• Semifree circle actions, Bott towers, and quasitoric manifolds