More Cappell-Shaneson spheres are standard

Details More Cappell-Shaneson spheres are standard More Cappell-Shaneson spheres are standard

2009-08-13

arxiv.org/abs/0908.1914v1

Algebraic and Geometric Topology 10 (2010), 1665-1681

Mathematics

Geometric Topology

10 pages, 2 figures

Scientific paper

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 strictly larger family is shown to be standard by a simpler method. 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, we give an example showing that Gluck twists can sometimes be undone using symmetries of fishtail neighborhoods.

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