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.

Notes on file formats

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

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.