Heegaard structures of manifolds in the Dehn " lling space Yo ' av Rieck *


We prove that after Dehn "lling an incompressible torus in the boundary of an a-cylindrical 3-manifold the Heegaard genus degenerates by at most one for all but "nitely many "llings. We do so by proving that for all but "nitely many "llings the core of the attached solid torus can be isotoped into the minimal Heegaard surface of the "lled manifold, we say… (More)

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