Homotopy Colimit of Quasi-join Diagrams

Abstract

We calculate the homotopy colimits of toric quasi-join diagrams that naturally appear in the shelling process of toric varieties [2]. Our objective is to give a sufficiently complete description of these spaces with the emphasis on those quasi-join diagrams which resemble the diagrams associated with lens spaces. The central result is a "recognition" theorem which is intended to serve as a principal result in a homological description of more complex, shellable spaces.