CELLULAR STRATIFIED SPACES

The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonzάlez, and Rudyak with the aim of constructing a cellular model of the configuration space of a sphere. Although the original aim was not achieved in the project, the notion of cellular stratified spaces turns out to be useful, at least, in the study of configuration spaces of graphs. In particular, the notion of totally normal cellular stratified spaces was used successfully in a joint work with the former students of the author [1] to study the homotopy type of configuration spaces of graphs with a small number of vertices.