Alberto Cavicchioli, Fulvia Spaggiari
On the topological structure of compact 5-manifolds

Comment.Math.Univ.Carolinae 34,3 (1993) 513-524.

Abstract:We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let $M$ be a closed connected orientable smooth $5$-manifold with free fundamental group. Then we prove that the number of distinct smooth $5$-manifolds homotopy equivalent to $M$ equals the $2$-nd Betti number (mod $2$) of $M$.

Keywords: colored graph, crystallization, genus, manifold, surgery, s-cobordism, normal invariants, homotopy type
AMS Subject Classification: 57N15, 57N65, 57R67