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An Exotic \({T_{1}\mathbb{S}^4}\) with Positive Curvature

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Abstract

We construct a metric with positive sectional curvature on a 7-manifold which supports an isometry group with orbits of codimension 1. It is a connection metric on the total space of an orbifold 3-sphere bundle over an orbifold 4-sphere. By a result of S. Goette, the manifold is homeomorphic but not diffeomorphic to the unit tangent bundle of the 4-sphere.

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Authors and Affiliations

  1. Mathematics Department, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN, 46556, USA

    Karsten Grove

  2. Dipartimento di Matematica Applicata, Via S. Marta, 3, I-50139, Firenze, Italy

    Luigi Verdiani

  3. Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104-6395, USA

    Wolfgang Ziller

Authors
  1. Karsten Grove
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  2. Luigi Verdiani
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  3. Wolfgang Ziller
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Corresponding author

Correspondence to Wolfgang Ziller.

Additional information

The first named author was supported in part by the Danish Research Council and by a grant from the National Science Foundation. The second named author was supported by GNSAGA. The third named author was supported by a grant from the National Science Foundation, and by CNPq-Brazil.

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Grove, K., Verdiani, L. & Ziller, W. An Exotic \({T_{1}\mathbb{S}^4}\) with Positive Curvature. Geom. Funct. Anal. 21, 499–524 (2011). https://doi.org/10.1007/s00039-011-0117-8

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  • DOI: https://doi.org/10.1007/s00039-011-0117-8

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