Non-Hamiltonian actions with isolated fixed points

TL;DR

This paper constructs a specific example of a six-dimensional symplectic manifold with a circle action that is non-Hamiltonian but has exactly 32 isolated fixed points, illustrating a unique symplectic phenomenon.

Contribution

It provides the first known example of a non-Hamiltonian symplectic circle action with isolated fixed points on a closed six-dimensional manifold.

Findings

Constructed a non-Hamiltonian symplectic circle action with 32 fixed points

Demonstrated existence of such actions on closed six-dimensional manifolds

Contributed to understanding symplectic actions beyond Hamiltonian cases

Abstract

We construct a non-Hamiltonian symplectic circle action on a closed, connected, six-dimensional symplectic manifold with exactly 32 fixed points.