= Excellent three-manifold
In the orientable case an excellent compact three-manifold is an <irreducible three-manifold> and a <boundary-irreducible three-manifold>, is not a ball, contains a two-sided properly embedded <incompressible surface>, and has every properly embedded incompressible zero-<Euler characteristic> surface a <boundary-parallel surface>. In particular it has no essential <annulus> or <torus>. These properties give lower bounds on the <Thurston norm> of classes with essential boundary.
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