On $5$-manifolds with free fundamental group and simple boundary links in $S^5$

Abstract

We classify compact oriented $5$-manifolds with free fundamental group and ${\pi }_2$ a torsion free abelian group in terms of the second homotopy group considered as ${\pi }_1$-module, the cup product on the second cohomology of the universal covering, and the second Stiefel-Whitney class of the universal covering. We apply this to the classification of simple boundary links of $3$-spheres in $S^5$. Using this we give a complete algebraic picture of closed $5$-manifolds with free fundamental group and trivial second homology group.

20 pages

Cited by in corpus (2)

• Suspension homotopy of $6$-manifolds
• Loop homotopy of $6$-manifolds over $4$-manifolds