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.
On the topological structure of compact 5-manifolds / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE. - ISSN 0010-2628. - STAMPA. - 34 (3):(1993), pp. 513-524.
On the topological structure of compact 5-manifolds
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
1993
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.
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