Cyclic symmetry and adic convergence in LagrangianFloer theory

TL;DR

This paper advances Lagrangian Floer cohomology by employing cyclic symmetry and adic convergence techniques to construct filtered A infinity algebras, enhancing the algebraic structures associated with Lagrangian submanifolds.

Contribution

It introduces cyclically symmetric filtered A infinity algebras for Lagrangian submanifolds using multisection techniques, improving previous constructions in Floer theory.

Findings

Construction of cyclically symmetric filtered A infinity algebras.

Development of local rigid analytic families of A infinity structures.

Analysis of homological algebra of pseudo-isotopy in cyclic A infinity context.

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.