Volume 21, issue 5 (2017)

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

Matthias Kreck and Yang Su

Geometry & Topology 21 (2017) 2989–3008

We classify compact oriented 5–manifolds with free fundamental group and π2 a torsion-free abelian group in terms of the second homotopy group considered as a π1–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 S5. Using this we give a complete algebraic picture of closed 5–manifolds with free fundamental group and trivial second homology group.

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fundamental group, normal bordism, simple boundary link
Mathematical Subject Classification 2010
Primary: 57R65
Secondary: 57R40
Received: 9 February 2016
Revised: 22 November 2016
Accepted: 8 January 2017
Published: 15 August 2017
Proposed: András I. Stipsicz
Seconded: Peter Teichner, Rob Kirby
Matthias Kreck
Hausdorff Research Institute for Mathematics
Universität Bonn
D-53115 Bonn
Yang Su
Institute of Mathematics
Chinese Academy of Sciences
Bejing, 100190