Geometriae Dedicata

, Volume 88, Issue 1, pp 199-210

First online:

Pointed Wiedersehen Metrics on Exotic Spheres and Diffeomorphisms of S6

  • Carlos E. DuránAffiliated withIVIC-Matemáticas

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Using a Kaluza–Klein-type procedure, an explicit metric h on an exotic sphere Σ7 is constructed, satisfying the Wiedersehen condition at a set of points diffeomorphic to S 1. The formulas for the geodesics allows the writing down of formulas for an explicit degree 1 diffeomorphism σ: S 6S 6 that is not isotopic to the identity.

closed geodesics exotic spheres exotic diffeomorphisms