collapse

In topology, a branch of mathematics, a collapse reduces a simplicial complex (or more generally, a CW complex) to a homotopy-equivalent subcomplex. Collapses, like CW complexes themselves, were invented by J. H. C. Whitehead. Collapses find applications in computational homology. Definition Let be an abstract simplicial complex. Suppose that are two simplices of such that the following two conditions are satisfied: in particular is a maximal face of and no other maximal face of contains