Wiedersehen metrics and exotic involutions of Euclidean spheres

Uwe Abresch; Carlos Duran; Thomas Puettmann; A. Rigas

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Wiedersehen metrics and exotic involutions of Euclidean spheres

Uwe Abresch·Carlos Duran·Thomas Puettmann·A. Rigas

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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 S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial elements in pi_1 Diff(S^5) and pi_1 Diff(S^13) and to provide explicit formulas for non-cancellation phenomena in group actions.

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BibTeX RIS

Uwe Abresch, Carlos Duran, Thomas Puettmann, A. Rigas. 2005-07-18. Wiedersehen metrics and exotic involutions of Euclidean spheres. https://arxiv.org/abs/math/0501091

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