Iterated integral and the loop product

TL;DR

This paper explores the connection between string topology and differential forms using Chen's iterated integrals and the cyclic bar complex, providing new insights into the algebraic structures underlying loop spaces.

Contribution

It introduces a novel relationship between string topology operations and iterated integrals within the framework of the cyclic bar complex.

Findings

Establishes a link between string topology and differential forms.

Provides a new algebraic perspective on loop space operations.

Enhances understanding of Chen's iterated integrals in topology.

Abstract

In this article we discuss a relation between the string topology and differential forms based on the theory of Chen's iterated integrals and the cyclic bar complex.