Non-compact totally peripheral 3-manifolds

Luke Harris and Peter Scott

Vol. 167 (1995), No. 1, 119–127

DOI: 10.2140/pjm.1995.167.119

Abstract

A 3-manifold is totally peripheral if every loop is freely homotopic into the boundary. It is shown that an orientable 3-manifold M is totally peripheral if and only if there is a boundary component F of M such that the inclusion of F in M induces a surjective map of fundamental groups. If M is non-orientable, there are essentially two counterexamples.

Mathematical Subject Classification 2000

Primary: 57N10

Milestones

Received: 10 July 1992

Revised: 15 November 1992

Published: 1 January 1995