Jeffrey Strom, Western Michigan University

Title:  RPT Models for Homotopy Fibers

Abstract:  The James reduced product construction gives a simple and immensely useful model for the suspension map $sigma : Xto OmegaSigma X$ adjoint to $mathrm{id}_{Sigma X}$. A great piece of evidence for the power of this construction is that it allows one to prove the Freudenthal suspension theorem (which estimates the connectivity of $sigma$) by textbf{just looking at the map}.

In the early 1960s, Sufian Husseini wrote several papers exploring spaces with structures inspired by the James reduced product construction. Sadly, even though these papers contain many great ideas, they have been largely overlooked. I recently took on the project of rebuilding this theory from the ground up with a more general and more modern point of view, and with a focus on the specific goal of modeling homotopy fibers.

In this talk, I’ll give an overview of this theory, and show that it can be used to give a `just look’ proof of the Blakers-Massey homotopy excision theorem.