Vol. 82, No. 2, 1979

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ISSN: 0030-8730
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/