About deformation retract - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T23:38:44Z http://mathoverflow.net/feeds/question/54299 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54299/about-deformation-retract About deformation retract daoi 2011-02-04T09:53:06Z 2011-02-04T11:09:38Z <p>Let $X\subset Y$ be CW-complexes. Denote $i\colon X\to Y$ be an inclusion map.</p> <p>Is it true that $i$ is deformation retract if and only if $i$ is homotopy equivalence?</p> <p>When I saw some papers about h-cobordism theorem, authors usually checks inclusion map is a homotopy equivalence to prove that inclusion map is deformation retract.</p> http://mathoverflow.net/questions/54299/about-deformation-retract/54303#54303 Answer by Chris Eagle for About deformation retract Chris Eagle 2011-02-04T11:09:38Z 2011-02-04T11:09:38Z <p>If $X$ is a subcomplex of $Y$ and the inclusion map is a homotopy equivalence, then $X$ is a deformation retract of $Y$. See for example proposition 0.16 and corollary 0.20 in <a href="http://www.math.cornell.edu/~hatcher/AT/ATpage.html" rel="nofollow">Hatcher</a>.</p>