Highly connected $7$-manifolds and non-negative sectional curvature

Pages 829-892 from Volume 191 (2020), Issue 3 by Sebastian Goette, Martin Kerin, Krishnan Shankar

Abstract

In this article, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm {SO}(3)$-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an $\mathrm{SO}(3)$-invariant metric of non-negative curvature.

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      pages = {27--31},
      issn = {0024-6093},
      mrclass = {57D55},
      mrnumber = {0307258},
      mrreviewer = {C. Henry Edwards},
      doi = {10.1112/blms/4.1.27},
      url = {https://doi.org/10.1112/blms/4.1.27},
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      }
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      author = {Wraith, David},
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      fjournal = {Journal of Differential Geometry},
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      number = {3},
      pages = {638--649},
      issn = {0022-040X},
      mrclass = {53C21 (57R60)},
      mrnumber = {1472892},
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      url = {https://doi.org/10.4310/jdg/1214459846},
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      }

Keywords
, , ,
Mathematical Subject Classification
Primary: Secondary: , ,
DOI
https://doi.org/10.4007/annals.2020.191.3.3
MR
4088352
zbMATH
07190305
Milestones
Received: 25 July 2017
Revised: 31 January 2020
Accepted: 31 January 2020
Published online: 15 April 2020

Authors

Sebastian Goette

Mathematisches Institut, Universität Freiburg, Germany

Martin Kerin

School of Mathematics, Statistics and Applied Mathematics, NUI Galway, Ireland

Krishnan Shankar

Department of Mathematics, The University of Oklahoma, Norman, OK, USA