The simplicial collapse of simplicial complexes -- John White and Mark Xue, October 14, 2003

A simplicial complex is a discrete tool for the study of homotopy types. It is well-known that every simplicial complex that posesses a collapse to a point has the homotopy type of a point, but the converse is not true. From observation of small sized simplicial complexes, one might infer that any arbitrary attempt to collapse a collapsible simplicial complex will succeed. We will demonstrate that in fact this is not true.