Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 20, pages 413-418.

The engulfing property for 3-manifolds

Graham A Niblo and Daniel T Wise

Abstract. We show that there are Haken 3-manifolds whose fundamental groups do not satisfy the engulfing property. In particular one can construct a pi_1-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

AMS subject classification. Primary: 20E26. Secondary: 20F34, 57M05, 57M25.

E-print: arXiv:math.GT/9810198

Submitted: 15 November 1997. Published: 27 October 1998.

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Graham A Niblo and Daniel T Wise
Faculty of Mathematical Studies, University of Southampton
Highfield, Southampton, SO17 1BJ, UK

Department of Mathematics, Cornell University
Ithaca, NY 14853, USA

Email: gan@maths.soton.ac.uk, daniwise@math.cornell.edu

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