2009/08/31 by Robert E. Gompf · 1 citation
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Calculus (dental) #Diffeomorphism #Framing (construction) #Geometric and Algebraic Topology #Geometry #Homogeneous space #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Pure mathematics #SPHERES #Simple (philosophy) #math.GT #msc:57R60
paper · pdf · doi:10.2140/agt.2010.10.1665
published as Algebr. Geom. Topol. 10 (2010) 1665-1681 · 11 pages, 2 figures. This (v2) is essentially the published version, with minor mathematical improvements over v1
openalex publication_date 2010/08/11 · arxiv created 2013/11/20 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Akbulut has recently shown that an infinite family of Cappell-Shaneson homotopy 4-spheres is diffeomorphic to the standard 4-sphere. In the present paper, a different method shows that a strictly larger family is standard. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akbulut and Kirby showing that the simplest example with untwisted framing is standard. Instead, hidden symmetries of the original Cappell-Shaneson construction are exploited. In the course of the proof, an example is given showing that Gluck twists can sometimes be undone using symmetries of fishtail neighborhoods.