Combinatorial Dehn surgery on cubed and Haken 3-manifolds

Iain R. Aitchison; J. Hyam Rubinstein

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arXiv · math/0008245

Combinatorial Dehn surgery on cubed and Haken 3-manifolds

Iain R. Aitchison·J. Hyam Rubinstein

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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.

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Iain R. Aitchison, J. Hyam Rubinstein. 2000-08-30. Combinatorial Dehn surgery on cubed and Haken 3-manifolds. https://arxiv.org/abs/math/0008245

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