Sewn-up r-link exteriors

Jim Hoste

Vol. 112 (1984), No. 2, 347–382

DOI: 10.2140/pjm.1984.112.347

Abstract

Suppose two solid handlebodies, each of genus r, are disjointly embedded in S³. If the interiors of the handlebodies are removed and the boundary components of the remaining space are identified via an orientation reversing homeomorphism, then a closed connected orientable 3-manifold results. Such a manifold is called a sewn-up r-link exterior. The main result of this paper is that a closed connected orientable 3-manifold M can be realized as a sewn-up r-link exterior if and only if the first homology of M is infinite.

The extend to which this theorem can be used to demonstrate Property R for knots is discussed.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57N10

Milestones

Received: 18 February 1982

Published: 1 June 1984