Incompressible one-sided surfaces in filled link spaces

Details Incompressible one-sided surfaces in filled link spaces Incompressible one-sided surfaces in filled link spaces

2008-07-30

arxiv.org/abs/0807.4795v1

Mathematics

Geometric Topology

11 pages

Scientific paper

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.

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