Almost positive curvature on the Gromoll-Meyer sphere
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Gromoll and Meyer have represented a certain exotic 7-sphere $Σ^7$ as a biquotient of the Lie group $G = Sp(2)$. We show for a 2-parameter family of left invariant metrics on $G$ that the induced metric on $Σ^7$ has strictly positive sectional curvature at all points outside four subvarieties of codimension $\geq 1$ which we describe explicitly.
8 pages, 1 figure, to appear in Proc. Amer. Math. Soc
8 pages, 1 figure, to appear in Proc. Amer. Math. Soc