The uniqueness of compact cores for 3-manifolds

Luke Harris and Peter Scott

Vol. 172 (1996), No. 1, 139–150

DOI: 10.2140/pjm.1996.172.139

Abstract

A compact core for a 3-manifold M is a compact sub-manifold N of M whose inclusion in M induces an isomorphism of fundamental groups. A uniqueness result for compact cores of orientable 3-manifolds is known. The authors show that compact cores are not unique in any reasonable sense for non-orientable 3-manifolds, but they prove a finiteness result about the number of possible cores.

Mathematical Subject Classification 2000

Primary: 57N10

Milestones

Received: 15 February 1993

Revised: 25 July 1993

Published: 1 January 1996