Vol. 80, No. 1, 1979

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ISSN: 0030-8730
Cancelling 1-handles and some topological imbeddings

Michael Freedman

Vol. 80 (1979), No. 1, 127–130
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
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/