EVENT DETAILS AND ABSTRACT

Title: On topological lifts of algebraic diagrams
Speaker: Professor James (Jim) Turner
Speaker Info: Calvin College
Brief Description:
Special Note:
Abstract:

In a program begun by W. Dwyer, D. Kan, and C. Stover, machinery was developed for determining whether a \Pi-algebra (a kind of twisted product of a graded Lie algebra with a group) can be realized by the homotopy groups of a space. One refinement of this program involves extending this machinery to address lifting diagrams of \Pi-algebras (such as arise from homotopy commutative diagrams of spaces) to diagrams of spaces that commute on the nose. Such a generalization opens the door to interpreting such things as Toda brackets as obstructions to making such extensions. In this talk, we describe such an extension of the Dwyer-Kan-Stover program and describe some aspects of computing the obstruction groups and potential connections to higher homotopy operations. This is joint work with David Blanc and Mark Johnson.