Quantum Cohomologies on Products of Cosymplectic Manifolds and Circles

In this paper we study the products of cosymplectic manifolds and a unit circle, which have natural symplectic structures. We have some relations on moduli spaces, Gromov–Witten invariants, and quantum cohomologies of cosymplectic manifolds and the products. As an example we examine the cosymplectic manifold M=S2×T×S1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=S^2\times T\times S^1$$\end{document} and the product M×S1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\times S^1$$\end{document}, and we also calculate their moduli spaces, Gromov–Witten invariants, and quantum cohomologies.