On a class of 5-manifolds with π₁=\mathbb Z with applications to knottings in S⁵

2014/11/06 by Matthias Kreck, Yang Su, Kreck, Matthias +1
Mathematics · #57R55 #57R65 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57R55 #msc:57R65

paper · pdf · doi:10.48550/arxiv.1411.1521

This paper has been withdrawn since we were informed by Professor Osamu Saeki that the applications to knots are already known

openalex publication_date 2014/11/06 · arxiv created 2014/11/12 · arxiv updated 2014/11/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We classify 5-manifolds with fundamental group \mathbb Z and π₂ 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 S³ ⊂ S⁵ 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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