Vol. 82, No. 2, 1979

Recent Issues
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Vol. 315: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
A converse to (Milnor-Kervaire theorem) ×R etc…

Michael Freedman

Vol. 82 (1979), No. 2, 357–369
Abstract

One of the most puzzling questions in low dimensional topology is which elements α π2(M), where M is a smooth compact 4-manifold, may be represented by a smoothly imbedded 2-sphere. This paper treats a stable version of the problem: When is there a smooth proper imbedding, h : S2 × RM × R by which the ends of S2 ×R are mapped to the ends of M × R, and for which the composition

 2 x→ (x,0) 2     h         π
S   −→  S  × R −→  M × R →  M

represents α?

Mathematical Subject Classification 2000
Primary: 57R95
Milestones
Received: 1 November 1976
Revised: 16 May 1978
Published: 1 June 1979
Authors
Michael Freedman
Station Q
Microsoft
CNSI Bldg. Rm 2245
University of California
Santa Barbara CA 93106-6105
United States
http://stationq.cnsi.ucsb.edu/~freedman/