Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 10, Number 3 (2010), 1665-1681.
More Cappell–Shaneson spheres are standard
Akbulut has recently shown that an infinite family of Cappell–Shaneson homotopy –spheres is diffeomorphic to the standard –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.
Algebr. Geom. Topol., Volume 10, Number 3 (2010), 1665-1681.
Received: 5 March 2010
Revised: 5 June 2010
Accepted: 8 June 2010
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R60: Homotopy spheres, Poincaré conjecture
Gompf, Robert E. More Cappell–Shaneson spheres are standard. Algebr. Geom. Topol. 10 (2010), no. 3, 1665--1681. doi:10.2140/agt.2010.10.1665. https://projecteuclid.org/euclid.agt/1513715148