# Homotopy type of a CW complex

The only dimension in which not every compact manifold is homeomorphic to a CW complex is $4$. Does every such manifold have the homotopy type of a CW complex?

• – Fernando Muro Jun 19 '15 at 21:42
• Yes, see Corollary A.12 of Hatcher's book. – Andy Putman Jun 19 '15 at 21:44