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A classification of 5-dimensional manifolds, souls of codimension two and non-diffeomorphic pairs · arXivDesk

1103.0099Mar 1, 201119 pages; in Proposition 3 the moduli space of nonnegative sectional curvature metrics equipped with the topology of uniform smooth convergence was replaced by a more general moduli space. This makes Proposition 3 stronger

A classification of 5-dimensional manifolds, souls of codimension two and non-diffeomorphic pairs

Sadeeb Ottenburger

Differential Geometry Geometric Topology

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Abstract

Let T(γ) be the total space of the canonical line bundle γover CP¹ and r an integer which is greater than one and coprime to six. We prove that L_r³× T(γ) admits an infinite sequence of metrics of nonnegative sectional curvature with pairwise non-homeomorphic souls, where L_r³ is the standard 3-dimensional lens space with fundamental group isomorphic to Z/r. We classify the total spaces of S¹-fibre bundles over S²× S² with fundamental group isomorphic to Z/r up to diffeomorphism and use these results to give examples of manifolds N which admit two complete metrics of nonnegative sectional curvature with souls S and S' of codimension two such that S and S' are diffeomorphic whereas the pairs (N,S) and (N,S') are not diffeomorphic. This solves a problem posed by I. Belegradek, S. Kwasik and R. Schultz.

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