Algorithms in $A_{\infty }$-algebras

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.

7 pages