On certain symplectic circle actions

Abstract

In this work we use localization formulas in equivariant cohomology to show that some symplectic actions on $6$-dimensional manifolds with a finite fixed point set must be Hamiltonian. Moreover, we show that their fixed point data (number of fixed points and their isotropy weights) is the same as in $S^2\times S^2 \times S^2$ equipped with a diagonal circle action, and we compute their cohomology rings.