2005/01/06 by Uwe Abresch, Carlos Duran, Abresch, Uwe +6
Mathematics · #53C22 #57R55 (Secondary) #57S17 #57S25 (Primary) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:53C22 #msc:57R55 #msc:57S17 #msc:57S25
paper · pdf · doi:10.48550/arxiv.math/0501091
17 pages, 5 figures, a QuickTime movie visualizing an exotic involution of S^5 is currently available at http://www.ruhr-uni-bochum.de/mathematik8/puttmann, revised version: corrections of typos, minor changes in the presentation, 1 reference added
openalex publication_date 2005/01/06 · arxiv created 2005/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient Sn/rho is a manifold that is homotopically equivalent but not diffeomorphic to RPn. We use these formulas for constructing explicit non-trivial elements in pi1 Diff(S5) and pi1 Diff(S13) and to provide explicit formulas for non-cancellation phenomena in group actions.