English

Pseudo-rotations and holomorphic curves

Symplectic Geometry 2019-08-08 v2 Dynamical Systems

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.

Keywords

Cite

@article{arxiv.1905.07567,
  title  = {Pseudo-rotations and holomorphic curves},
  author = {Erman Cineli and Viktor L. Ginzburg and Basak Z. Gurel},
  journal= {arXiv preprint arXiv:1905.07567},
  year   = {2019}
}

Comments

27 pages; minor corrections made

R2 v1 2026-06-23T09:11:30.662Z