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

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].

### 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
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