Cyclic symmetry and adic convergence in Lagrangian Floer theory

In this article we use a continuous family of multisections of the moduli space of pseudoholomorphic discs to partially improve the construction of the Lagrangian Hoer cohomology of [11] in the case of R coefficient. Namely, we associate a 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)-structures associated to a (family of) Lagrangian submanifolds. We include the study of homological algebra of pseudoisotopy of cyclic (filtered) A(infinity)-algebras.