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 ) . {\displaystyle \tau (f).} \tau (f).
See also
Discrete Morse theory
References
Cohen, Marshall M. (1973), A course in simple-homotopy theory, Berlin, New York: Springer-Verlag, ISBN 978-3-540-90055-9, MR 0362320
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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