Comparing Heegaard splittings of non- Haken 3-manifolds
- H. Rubinstein, M. Scharlemann
- Topology, 35(4):1005–1026,
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided Heegaard splittings, this result can be used to complete the classification of one-sided splittings of (2p, q) fillings of Figure 8 knot space: determining that fillings with | 2p q | < 3 have two non-isotopic geometrically incompressible one-sided splitting surfaces.