# Pseudo-rotations and holomorphic curves

## TL;DR

This paper proves a variant of the Chance-McDuff conjecture for pseudo-rotations, showing that certain symplectic manifolds with pseudo-rotations have deformed quantum products and non-zero Gromov-Witten invariants.

## Contribution

It establishes a new link between pseudo-rotations and quantum cohomology in symplectic manifolds under specific conditions.

## Key findings

- Pseudo-rotations imply non-trivial Gromov-Witten invariants.
- Manifolds with pseudo-rotations have deformed quantum products.
- Results apply to weakly monotone manifolds with minimal Chern number > 1.

## Abstract

We prove a variant of the Chance-McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular, some non-zero Gromov-Witten invariants. The only assumptions on the manifold are that it is weakly monotone and that its minimal Chern number is greater than one. The conditions on the pseudo-rotation are expressed in terms of the linearized flow at one of the fixed points and hypothetically satisfied for most (but not all) pseudo-rotations.