Cyclic symmetry and adic convergence in LagrangianFloer theory

Abstract

In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta-Ono. Namely we associate cyclically symmetric filtered A infinity algebra to every relatively spin Lagrangian submanifold. We use the same trick to construct a local rigid analytic family of filtered A infinity structure associated to a (family of) Lagrangian submanifolds. We include the study of homological algebra of pseudo-isotopy of cyclic (filtered) A infinity algebra.