A twisted tale of cochains and connections

TL;DR

This paper explores the deep connections between Massey products, A-infinity structures, and homotopy invariants in differential graded algebras, highlighting historical developments and personal tributes within the field of higher homotopy algebra.

Contribution

It clarifies the relationship between Kadeisvili's work on A-infinity structures and earlier contributions by Gugenheim and Chen, emphasizing their significance in homotopy theory.

Findings

Massey products are homotopy invariants in a specific sense.

Kadeisvili's work reveals Massey products as shadows of A-infinity-structures.

The paper highlights the convergence of ideas in homotopy algebra.

Abstract

Early in the history of higher homotopy algebra, it was realized that Massey products are homotopy invariants in a special sense, but it was the work of Tornike Kadeisvili that showed they were but a shadow of an A-infinity-structure on the homology of a differential graded algebra. Here we relate his work to that of Victor Gugenheim and K.T. (Chester) Chen. This paper is a personal tribute to Tornike and the Georgian school of homotopy theory as well as to Gugenheim and Chen, who unfortunately are not with us to appreciate this convergence.