Vol. 94, No. 1, 1981

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Homology cobordisms of 3-manifolds, knot concordances, and prime knots

Charles Livingston

Vol. 94 (1981), No. 1, 193–206
Abstract

There is a close relation between link concordances and homology cobordisms of 3-manifolds. Using this relationship we will prove that every closed, orientable 3-manifold is homology cobordant to an irreducible 3-manifold. Essentially the same construction will be used to prove that every knot in S3 is concordant to a prime knot.

Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57N10
Milestones
Received: 2 April 1979
Published: 1 May 1981
Authors
Charles Livingston
Department of Mathematics
Indiana University
Rawles Hall
Bloomington IN 47405-5701
United States