Yasin Uskuplu, USC

Title: A Primer on A_infinity Algebras II

Abstract: In this talk, I will continue to introduce A_infinity algebras to a broad audience from where I left off in the first talk. In other words, I will start with A_infinity homotopy and then introduce one of the applications, called Homological Perturbation Lemma (HPL), which endows a cochain complex with an A_infinity algebra structure. One of its significant consequences is that in A_infinity world, any quasi-isomorphism has a quasi-inverse up to homotopy, which is not necessarily true in the dg category of cochain complexes. I also want to touch upon the formality of dg algebras closely related to HPL. I aim to provide some examples of non-formal dg algebras, such as Borromean rings or Brunnian links in general.