Homotopy excision and cellularity

Abstract

Consider a push-out diagram of spaces C <-- A --> B, construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object A. We compare the difference between A and this homotopy pull-back. This difference is measured in terms of the homotopy fibers of the original maps. Restricting our attention to the connectivity of these maps, we recover the classical Blakers-Massey Theorem.

22 pages, we took special care in this revised version in distinguishing fiber sets from single fibers, in indicating what we mean by the loop space on a possibly non-connected and unpointed space, thus smoothing the exposition