On 5–manifolds with free fundamental group and simple boundary links in S5

Kreck, Matthias¹ ; Su, Yang²

¹ Hausdorff Research Institute for Mathematics, Universität Bonn, D-53115 Bonn, Germany
² Institute of Mathematics, Chinese Academy of Sciences, Bejing, 100190, China

Geometry & topology, Tome 21 (2017) no. 5, pp. 2989-3008.

Résumé

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 a ${\pi }_1$–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.

Détail

DOI : 10.2140/gt.2017.21.2989

Classification : 57R65, 57R40
Keywords: fundamental group, normal bordism, simple boundary link

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