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26 April 2024
 
  » arxiv » math.GT/0501091

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Wiedersehen metrics and exotic involutions of Euclidean spheres
Uwe Abresch ; Carlos Duran ; Thomas Puettmann ; A. Rigas ;
Date 6 Dec 2004
Subject Geometric Topology; Differential Geometry MSC-class: 57S25 (Primary), 53C22, 57S17, 57R55 (Secondary) | math.GT math.DG
AffiliationRuhr-Universitaet Bochum), Carlos Duran (Unicamp), Thomas Puettmann (Ruhr-Universitaet Bochum), A. Rigas (Unicamp
AbstractWe 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.
Source arXiv, math.GT/0501091
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