Wiedersehen metrics and exotic involutions of Euclidean spheres

✍ Scribed by Abresch, U; Durán, C; Püttmann, T; Rigas, A

• Book ID: 118740363
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2007
• Tongue: English
• Weight: 295 KB
• Volume: 2007
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2007.025

✦ Synopsis

We provide explicit, simple, geometric formulas for free involutions r of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S n =r is a manifold that is homotopically equivalent but not di¤eomorphic to RP n . We use these formulas for constructing explicit non-trivial elements in p 1 Di¤ðS 5 Þ and p 1 Di¤ðS 13 Þ and to provide explicit formulas for non-cancellation phenomena in group actions.