The Gromov-Witten class and a perturbation theory in algebraic geometry

We propose a method to construct the virtual fundamental class based on the "Kontsevich principle," i.e., we formulate the notion of quasi manifold structrue and establish a way to obtain the fundamental class from it. Also, we show that there is a natural quasi manifold structure on the moduli stack of stable maps, and thus we arrive at the new construction of the Gromov-Witten class. We also prove the fixed point formula for our Gromov-Witten class.