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Generalized Heegaard Splittings
rV JSJ Heegaard Comparisons
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1-complex 1-handles 2-sphere aligned Seifert fiber ambient isotopy annulus component arc-compressing disk attaching map base surface boundary component bounds a disk bundle complexity component of Si(t components of dL compressing disk connected 3-manifold connected compression body contained contradiction curve in Si(t d-Ai d-Bi definition embedded disk essential annuli essential in Si(t Euler characteristic fiber space component finish the proof fr(TV fr(W handlebody Heegaard genus Heegaard surface homeomorphic homotopic I-bundle incompressible boundary inessential injective irreducible 3-manifold irreducible generalized Heegaard irreducible Heegaard splittings isotop JSJ decomposition lemma V.7 Lens spaces manifold Martin Scharlemann meets dM number of components orientable 3-manifold orientable surface properly embedded Recall regular neighborhood S U F Scharlemann Seifert fiber space side of Si(t simple closed curves solid torus spine strongly irreducible Heegaard subinterval submanifold surface of Euler sweepout Theorem IV.5 topological toral torus xl U D V Usn Bn valence(u vertex