Special Hamiltonian $S^1$-actions on symplectic 4-manifolds

Mei-Lin Yau

Special Hamiltonian $S^1$-actions on symplectic 4-manifolds

Symplectic Geometry 2026-01-06 v4

Authors: Mei-Lin Yau

Abstract

In this paper we consider symplectic 4-manifolds $(M,\omega)$ with $c_1(M,\omega)=0$ which admit a Hamiltonian $S^1$ -action together with an equivariant Maslov condition on orbits of the group action. We call such spaces {\em special Hamiltonian $S^1$ -spaces}. It turns out that there are no compact special Hamiltonian $S^1$ -spaces. We classify all exact special Hamiltonian $S^1$ -spaces and show that all of them admit the structure of a Stein surface.

Keywords

symplectic 4-manifolds Hamiltonian S^1-action Maslov condition Stein surface classification

Cite

@article{arxiv.2212.00991,
  title  = {Special Hamiltonian $S^1$-actions on symplectic 4-manifolds},
  author = {Mei-Lin Yau},
  journal= {arXiv preprint arXiv:2212.00991},
  year   = {2026}
}

Comments

v.4, 31 pages

Related papers

View all related →