Wiedersehen metrics and exotic involutions of Euclidean spheres
Abstract
We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient Sn/rho is a manifold that is homotopically equivalent but not diffeomorphic to RPn. We use these formulas for constructing explicit non-trivial elements in pi1 Diff(S5) and pi1 Diff(S13) and to provide explicit formulas for non-cancellation phenomena in group actions.
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