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

Charles Livingston

Vol. 94 (1981), No. 1, 193–206

DOI: 10.2140/pjm.1981.94.193

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