Arnold conjecture over integers
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.
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!