, Volume 21, Issue 3, pp 499-524
Date: 13 Apr 2011

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.

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.