Combinatorial Dehn surgery on cubed and Haken 3-manifolds. (English) Zbl 0948.57016

Aitchison, I. R.; Rubinstein, J. H.

Hass, Joel (ed.) et al., Proceedings of the Kirbyfest, Berkeley, CA, USA, June 22-26, 1998. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 2, 1-21 (1999).

This paper describes a combinatorial condition for when immersed or embedded incompressible surfaces in compact 3-manifolds with tori boundary components remain incompressible after Dehn surgery. The result is applied to hierarchies and cubed manifolds.
For the entire collection see [Zbl 0939.00055].

Reviewer: R.E.Stong (Charlottesville)

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
57M50	General geometric structures on low-dimensional manifolds
57R65	Surgery and handlebodies

Keywords:

incompressible surfaces; hierarchies; cubed manifolds