Abstract

In this article, we define an action of \hat{\Bbb Z} on the A_{\infty} category whose objects are rational Lagrangian submanifolds together with some other data. The group \hat{\Bbb Z} is a Galois group of the (universal) Novikov ring (field) over Laurent polynomial field. By mirror symmetry it will corresponds to the algebraic fundamental group of a punctured disk which parametrize the maximal degenerate family of the mirror complex manifold.