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.
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