An integer optimization problem for non-Hamiltonian periodic flows

TL;DR

This paper introduces an integer optimization approach to estimate the minimum number of equilibrium points in certain non-Hamiltonian symplectic flows on specific compact manifolds, confirming a longstanding conjecture in multiple dimensions.

Contribution

It formulates a new integer optimization problem to bound equilibrium points and verifies a conjecture for unitary manifolds in several dimensions.

Findings

Confirmed the conjecture for dimensions 8, 10, 12, 14, 18, 20, 22.

Established a lower bound B(n) for equilibrium points.

Linked symplectic topology with integer optimization techniques.

Abstract

Let C be the class of compact 2n-dimensional symplectic manifolds M for which the first or (n-1) Chern class vanish. We point out an integer optimization problem to find a lower bound B(n) on the number of equilibrium points of non-Hamiltonian symplectic periodic flows on manifolds M in C. As a consequence, we confirm in dimensions 2n in {8,10,12,14,18,20, 22} a conjecture for unitary manifolds made by Kosniowski in 1979 for the subclass C.