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