Highly connected 7-manifolds, the linking form and non-negative\n curvature

2020/03/10 by Sebastian Goette, Goette, Sebastian, Martin Kerin +3
Mathematics · Medicine · #57R19 #57R30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #primary: 53C20 #secondary: 55R55

paper · pdf · doi:10.48550/arxiv.2003.04907

openalex publication_date 2020/03/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In a recent article, the authors constructed a six-parameter family of highly\nconnected 7-manifolds which admit an SO(3)-invariant metric of non-negative\nsectional curvature. Each member of this family is the total space of a Seifert\nfibration with generic fibre S³ and, in particular, has the cohomology ring\nof an S³-bundle over S⁴. In the present article, the linking form of\nthese manifolds is computed and used to demonstrate that the family contains\ninfinitely many manifolds which are not even homotopy equivalent to an\nS³-bundle over S⁴, the first time that any such spaces have been shown to\nadmit non-negative sectional curvature.\n

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