Wiedersehen metrics and exotic involutions of Euclidean spheres

@inproceedings{Abresch2005WiedersehenMA,
  title={Wiedersehen metrics and exotic involutions of Euclidean spheres},
  author={Uwe Abresch and Carlos E. Dur{\'a}n and Thomas Puettmann and Alcib{\'i}ades Rigas},
  year={2005}
}
Abstract We provide explicit, simple, geometric formulas for free involutions ρ of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient Sn/ρ is a manifold that is homotopically equivalent but not diffeomorphic to . We use these formulas for constructing explicit non-trivial elements in π1 Diff(S 5) and π1 Diff(S 13) and to provide explicit formulas for non-cancellation phenomena in group actions. 

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