On a class of $5$-manifolds with $π_1=\mathbb Z$ with applications to knottings in $S^5$

Matthias Kreck; Yang Su

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arXiv · 1411.1521

On a class of $5$-manifolds with $π_1=\mathbb Z$ with applications to knottings in $S^5$

Matthias Kreck·Yang Su

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Abstract

We classify $5$-manifolds with fundamental group $\mathbb Z$ and $π_{2}$ a finitely generated abelian group in terms of the cup product on the second cohomology of the universal covering. The classification result is applied to study simple knots $k \colon S^{3} \subset S^{5}$ and the question, which compact topological or smooth orientable $5$-manifold is a topological or smooth fibre bundle over the circle with simply-connected fibre.

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BibTeX RIS

Matthias Kreck, Yang Su. 2014-11-12. On a class of $5$-manifolds with $π_1=\mathbb Z$ with applications to knottings in $S^5$. https://arxiv.org/abs/1411.1521

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