English

Arnold conjecture over integers

Symplectic Geometry 2022-09-20 v1 Algebraic Topology Dynamical Systems Geometric Topology

Abstract

For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth global Kuranishi charts. This generalizes a recent work of Abouzaid-McLean-Smith, which might be of independent interest.

Keywords

Cite

@article{arxiv.2209.08599,
  title  = {Arnold conjecture over integers},
  author = {Shaoyun Bai and Guangbo Xu},
  journal= {arXiv preprint arXiv:2209.08599},
  year   = {2022}
}

Comments

168 pages, 2 figures. Comments welcome!

R2 v1 2026-06-28T01:32:24.021Z