Non-symplectic smooth circle actions on symplectic manifolds

TL;DR

This paper introduces methods to construct smooth circle actions on symplectic manifolds that have fixed point sets or isotropy sets which are not symplectic, demonstrating actions incompatible with any symplectic form.

Contribution

It provides new techniques for constructing smooth circle actions with non-symplectic fixed point or isotropy sets on symplectic manifolds, expanding understanding of symplectic action constraints.

Findings

Constructed smooth circle actions with non-symplectic fixed point sets

Demonstrated these actions are incompatible with any symplectic form

Expanded the class of known symplectic manifold actions

Abstract

We present some methods to construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or non-symplectic cyclic isotropy point sets. All such actions are not compatible with any symplectic form.