Online Talk

Loop homology algebra (with respect to the Pontryagin multiplication) often provides insight into the homotopy type of a topological space; in particular, it determines its rational homotopy groups. For the moment-angle complex corresponding to a flag simplicial complex, this algebra is the "commutator subalgebra" of a certain partially commutative algebra. I will outline a homological approach which gives a presentation of this subalgebra by multiplicative generators and relations. This approach works more generally, e.g. for quasitoric manifolds or polyhedral products of the form (CΩX,ΩX)^K.

In the second part of the talk, I will discuss an approach to conjectural generalisations of the Hilton-Milnor theorem to polyhedral products which uses loop homology and Grobner-Shirshov bases for Lie (super)algebras. This is an ongoing research project with Lewis Stanton.