Algorithms in $A_\infty$-algebras

TL;DR

This paper surveys algorithmic methods for computing explicit $A_ abla$-algebra structures across various mathematical contexts, including homotopy retractions, group cohomology, and persistent homology.

Contribution

It provides a comprehensive overview of recent algorithmic developments in calculating $A_ abla$-algebra structures in different areas of algebra and topology.

Findings

Summarizes algorithms for homotopy retractions

Reviews methods in group cohomology

Discusses applications in persistent homology

Abstract

Building on Kadeishvili's original theorem inducing $A_\infty$-algebra structures on the homology of dg-algebras, several directions of algorithmic research in $A_\infty$-algebras have been pursued. In this paper we will survey work done on calculating explicit $A_\infty$-algebra structures from homotopy retractions; in group cohomology; and in persistent homology.