On critical kernels

We propose a method for collapsing simplicial complexes. For that purpose, we introduce the notion of an essential face, and the one of a core of a cell. Then, we define the critical kernel of a complex. Our main result is that the critical kernel of a given complex X is a collapse of X. We extend this result by giving a necessary and sufficient condition which characterizes a certain class of subcomplexes of X which contain the critical kernel of X. In particular, any complex which belongs to this class is homotopy equivalent to X.