On the homotopy links of stratified cell complexes

Abstract: Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in particular to investigate the stratified homotopy hypothesis, a more general version of this result pertaining to stratified cell complexes is needed. Here we prove that, given a stratified cell complex $X$, the generalized homotopy links can be computed in terms of certain subcomplexes of a subdivision of $X$. As a consequence, it follows that homotopy links map certain pushout diagrams of stratified cell complexes into homotopy pushout diagrams. This result is crucial to the development of (semi-)model structures for stratified homotopy theory in which geometric examples of stratified spaces, such as Whitney stratified spaces, are bifibrant.