Cappell-Shaneson homotopy spheres are standard

2009/07/01 by Selman Akbulut, Akbulut, Selman · 2 citations
Mathematics · #57R65 #58A05 #58D27 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0907.0136

openalex publication_date 2009/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that an infinite sequence of homotopy 4-spheres constructed by Cappell-Shaneson are all diffeomorphic to S⁴. This generalizes previous results of Akbulut-Kirby and Gompf.

Cited by

• New Homotopy 4-Spheres
• Fibered knots and Property 2R, II

Related

• A novel construction of homotopy 4-spheres and real projective 4-spaces à la Cappell-Shaneson
• Nash homotopy spheres are standard
• Ideal classes and Cappell-Shaneson homotopy 4-spheres
• On a homotopy 4-sphere
• Smooth homotopy 4-sphere