Collapse (topology)

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.

[1] Collapses find applications in computational homology.

then this is called an elementary collapse.

A simplicial complex that has a sequence of collapses leading to a point is called collapsible.

Every collapsible complex is contractible, but the converse is not true.

This definition can be extended to CW-complexes and is the basis for the concept of simple-homotopy equivalence.