Embedding open 3-manifolds in compact 3-manifolds

Robert A. Messer and Alden H. Wright

Vol. 82 (1979), No. 1, 163–177

DOI: 10.2140/pjm.1979.82.163

Abstract

We consider open 3-manifolds that are monotone unions of compact 3-manifolds each bounded by a torus. We give necessary and sufficient conditions for embedding such an open 3-manifold in a compact 3-manifold. We also show that if the open 3-manifold embeds in a compact 3-manifold, then it embeds in a compact 3-manifold as the complement of the intersection of a decreasing sequence of solid tori.

Mathematical Subject Classification 2000

Primary: 57N10

Milestones

Received: 3 November 1977

Published: 1 May 1979