Collapsibility

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.

Let ${\displaystyle K}$ be an abstract simplicial complex.

Suppose that ${\displaystyle \tau ,\sigma \in K}$ such that the following two conditions are satisfied:

(i) ${\displaystyle \tau \subset \sigma }$, in particular ${\displaystyle \dim \tau <\dim \sigma }$;

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