Iterated integrals on the Legendre family of elliptic curves (2507.13790v1)

Abstract: K.T. Chen showed that iterated integrals give comparison isomorphisms between the cohomologies of bar complexes and fundamental group rings. This led to the development of an algebraic-geometric approach to studying periods given by iterated integrals. In this paper we consider an analogue of this comparison isomorphism theorem for iterated integrals on the Legendre family.