Simple-homotopy equivalence

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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, τ(f).

[edit] References

• Cohen, Marshall M. (1973), A course in simple-homotopy theory, Berlin, New York: Springer-Verlag, MR0362320, ISBN 978-3-540-90055-9