Algorithms in A _∞-algebras

Abstract

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

The Mathematics of Tie Knots

“…They created a new formal language to do so, and counted 266, 682 tie-knots that seem tie-able. Vejdemo-Johansson [6] hosts an online tie knot generation toy which allows the user to randomly pick one these neck ties. In addition, Vejdemo-Johansson believes that their count of neck ties is a lower bound.…”