Pulling back the Gromoll-Meyer construction and models of exotic spheres

2010/10/28 by Llohann D. Sperança, Sperança, Llohann D.
Mathematics · #57R60 #57S15 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #math.AT #math.DG #math.GT #msc:57R60 #msc:57S15

paper · pdf · doi:10.48550/arxiv.1010.6039

14 pages

openalex publication_date 2010/10/28 · arxiv created 2014/05/08 · arxiv updated 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we generalize the Gromoll-Meyer construction of an exotic 7-sphere by producing geometric models of exotic 8, 10 and Kervaire spheres as quotients of sphere bundles over spheres by free isometric actions. We give a geometric application at the end.

Related

• An infinite family of Gromoll-Meyer spheres
• Curvature of an exotic 7-sphere
• An exotic sphere with positive curvature
• Isoparametric functions and exotic spheres
• A co-dimensional 3 sub-Riemannian structure on Gromoll-Meyer exotic sphere