Cellular Stratified Spaces II: Basic Constructions

Abstract

This is a sequel to [1106.3772], in which a systematic study of cellular stratified spaces and related concepts was initiated. In this paper, we study important operations on cellular and stellar stratified spaces, including taking subspaces, subdivisions, and products. We also introduce a procedure which extends the classical duality for simplicial complexes. The results in this paper will be used to construct "Salvetti-type" models for configuration spaces.