Geometriae Dedicata

, Volume 88, Issue 1, pp 199–210

Pointed Wiedersehen Metrics on Exotic Spheres and Diffeomorphisms of S6


  • Carlos E. Durán
    • IVIC-Matemáticas

DOI: 10.1023/A:1013163427655

Cite this article as:
Durán, C.E. Geometriae Dedicata (2001) 88: 199. doi:10.1023/A:1013163427655


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

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© Kluwer Academic Publishers 2001