## Geometry & Topology

### 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 $π2$ 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

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

Dates
Revised: 22 November 2016
Accepted: 8 January 2017
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859279

Digital Object Identifier
doi:10.2140/gt.2017.21.2989

Mathematical Reviews number (MathSciNet)
MR3687112

Zentralblatt MATH identifier
1377.57033

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

#### Citation

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. https://projecteuclid.org/euclid.gt/1510859279

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