Geometry & Topology

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

Matthias Kreck and Yang Su

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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.

Article information

Geom. Topol., Volume 21, Number 5 (2017), 2989-3008.

Received: 9 February 2016
Revised: 22 November 2016
Accepted: 8 January 2017
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R65: Surgery and handlebodies
Secondary: 57R40: Embeddings

fundamental group normal bordism simple boundary link


Kreck, Matthias; Su, Yang. On $5$–manifolds with free fundamental group and simple boundary links in $S^5$. Geom. Topol. 21 (2017), no. 5, 2989--3008. doi:10.2140/gt.2017.21.2989.

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