A converse to (Milnor-Kervaire theorem) ×R etc…

Michael Freedman

Vol. 82 (1979), No. 2, 357–369

DOI: 10.2140/pjm.1979.82.357

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 × R↪M × R by which the ends of S² ×R are mapped to the ends of M × R, and for which the composition

represents α?

Mathematical Subject Classification 2000

Primary: 57R95

Milestones

Received: 1 November 1976

Revised: 16 May 1978

Published: 1 June 1979