In mathematics, particularly the area of topology, a **simple-homotopy equivalence** is a refinement of the concept of homotopy equivalence. Two CW-complexes are simple-homotopy equivalent if they are related by a sequence of collapses and expansions (inverses of collapses), and a homotopy equivalence is a simple homotopy equivalence if it is homotopic to such a map.

The obstruction to a homotopy equivalence being a simple homotopy equivalence is the Whitehead torsion,

## See also

## References

- Cohen, Marshall M. (1973),
*A course in simple-homotopy theory*, Berlin, New York: Springer-Verlag, ISBN 978-3-540-90055-9, MR 0362320