Cancelling 1-handles and some topological imbeddings

Michael Freedman

Vol. 80 (1979), No. 1, 127–130

DOI: 10.2140/pjm.1979.80.127

Abstract

In this note we use the existence of a certain type of handle decomposition (see corollary) for compact simply connected P. L. 4-manifolds and R. Edwards results on the double suspension conjecture to prove:

Theorem 2. Let α ∈ H₂(M;Z) where M is a compact simply connected P. L. 4-manifold. Then there is a proper topological imbedding (possible nonlocally flat) 𝜃 : S² ×R → M ×R (mapping ends to ends) with 𝜃_∗[S² ×R] = α ∈ H₂(M ×R;Z). α is the image of α under ×R. Proper, here, means inverse images of compact sets are compact.

Mathematical Subject Classification 2000

Primary: 57N35

Milestones

Received: 20 October 1976

Revised: 9 August 1977

Published: 1 January 1979