A minimal Brieskorn 5sphere in the GromollMeyer sphere and its applications
Abstract
We recognize the GromollMeyer sphere Sigma^7 as the geodesic join of a simple closed geodesic and a minimal subsphere Sigma^5, which can be equivariantly identified with the Brieskorn sphere W^5_3. As applications we in particular determine the full isometry group of Sigma^7, classify all closed subgroups that act freely, determine the homotopy type of the corresponding orbit spaces, identify the HirschMilnor involution in dimension 5 with the Calabi involution of W^5_3, and obtain explicit formulas for diffeomorphisms between the Brieskorn spheres W^5_3 and W^13_3 with standard Euclidean spheres.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606769
 Bibcode:
 2006math......6769D
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology