Volume 10, issue 3 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
More Cappell–Shaneson spheres are standard

Robert E Gompf

Algebraic & Geometric Topology 10 (2010) 1665–1681
Abstract

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.

Keywords
homotopy sphere, $4$–manifold, Poincare Conjecture, logarithmic transformation, Gluck construction
Mathematical Subject Classification 2000
Primary: 57R60
References
Publication
Received: 5 March 2010
Revised: 5 June 2010
Accepted: 8 June 2010
Published: 11 August 2010
Authors
Robert E Gompf
Department of Mathematics
The University of Texas at Austin
1 University Station C1200
Austin, TX 78712-0257
USA