A minimal Brieskorn 5-sphere in the Gromoll-Meyer sphere and its applications
Duran, Carlos · Puettmann, Thomas
Original · EN
We recognize the Gromoll-Meyer sphere Sigma⁷ as the geodesic join of a simple closed geodesic and a minimal subsphere Sigma⁵, which can be equivariantly identified with the Brieskorn sphere W⁵₃. As applications we in particular determine the full isometry group of Sigma⁷, classify all closed subgroups that act freely, determine the homotopy type of the corresponding orbit spaces, identify the Hirsch-Milnor involution in dimension 5 with the Calabi involution of W⁵₃, and obtain explicit formulas for diffeomorphisms between the Brieskorn spheres W⁵₃ and W¹3₃ with standard Euclidean spheres.
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