Volume 1 (1998)

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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
The engulfing property for 3–manifolds

Graham A Niblo and Daniel T Wise

Geometry & Topology Monographs 1 (1998) 413–418
DOI: 10.2140/gtm.1998.1.413

arXiv: math.GT/9810198

Abstract
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We show that there are Haken 3–manifolds whose fundamental groups do not satisfy the engulfing property. In particular one can construct a π1–injective immersion of a surface into a graph manifold which does not factor through any proper finite cover of the 3–manifold.

Keywords
double coset decompositions, subgroup separability, 3–manifolds, engulfing property
Mathematical Subject Classification
Primary: 20E26
Secondary: 20F34, 57M05, 57M25
References
Publication
Received: 15 November 1997
Published: 27 October 1998
Authors
Graham A Niblo
Faculty of Mathematical Studies
University of Southampton
Highfield, Southampton
SO17 1BJ
United Kingdom
Daniel T Wise
Department of Mathematics
Cornell University
Ithaca NY 14853
USA