New homotopy theoretical invariants and Hopf algebras Seminar

The talks is based on recent results arising form joint work with Victor Buchstaber.
For an arbitrary topological space X, the based loop space homology H is a Hopf algebra. We introduce a new homotopy invariant of a topological space X taking for its value the isomorphism class (over the integers) of the Hopf algebra H.

Studying different Hopf algebra structures on a tensor algebra T(V), we analyse homotopy types of topological spaces and detect a new structural property of the cup product.

We further investigate relations between this new homotopy invariant and well known classical invariants and constructions in homotopy theory and algebra.