Simple-homotopy equivalence
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
This article is issued from
Wikipedia.
The text is licensed under Creative Commons - Attribution - Sharealike.
Additional terms may apply for the media files.