Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 1, pages 1-21.

Combinatorial Dehn surgery on cubed and Haken 3-manifolds

IR Aitchison and JH Rubinstein

Abstract. A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3--manifolds with tori boundary components remain incompressible after Dehn surgery. A combinatorial characterisation of hierarchies is described. A new proof is given of the topological rigidity theorem of Hass and Scott for 3--manifolds containing immersed incompressible surfaces, as found in cubings of non-positive curvature.

Keywords. 3-manifold, Dehn surgery, cubed manifold, Haken manifold

AMS subject classification. Primary: 57M50. Secondary: 57N10.

E-print: arXiv:math.GT/0008245

Submitted: 24 September 1998. (Revised: 14 November 1999.) Published: 22 November 1999.

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IR Aitchison and JH Rubinstein
Department of Mathematics and Statistics, University of Melbourne
Parkville, Vic 3052, Australia
Email: iain@ms.unimelb.edu.au, rubin@ms.unimelb.edu.au

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