2008/07/30 by Loretta Bartolini, Bartolini, Loretta
Mathematics · #57M27 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27 #msc:57N10
paper · pdf · doi:10.48550/arxiv.0807.4795
11 pages
arxiv created 2008/07/30 · arxiv updated 2009/12/01
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.