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Incompressible one-sided surfaces in even fillings of Figure 8 knot space

In the closed, non-Haken, hyperbolic class of examples generated by (2p,q) Dehn fillings of Figure 8 knot space, the geometrically incompressible one-sided surfaces are identified by the filling ratio p/q and determined to be unique in all cases. When applied to one-sided Heegaard splittings, this can be used to classify all geometrically incompressible splittings in this class of closed, hyperbolic examples; no analogous classification exists for two-sided Heegaard splittings.