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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

Combinatorial Dehn surgery on cubed and Haken 3–manifolds

Iain R Aitchison and J Hyam Rubinstein

Geometry & Topology Monographs 2 (1999) 1–21

DOI: 10.2140/gtm.1999.2.1

arXiv: math.GT/0008245

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

Mathematical Subject Classification

Primary: 57M50

Secondary: 57N10

References
Publication

Received: 24 September 1998
Revised: 14 November 1999
Published: 22 November 1999

Authors
Iain R Aitchison
Department of Mathematics and Statistics
University of Melbourne
Parkville
Victoria 3052
Australia
J Hyam Rubinstein
Department of Mathematics and Statistics
University of Melbourne
Parkville
Victoria 3052
Australia